Learn Hardcore Japanese: kyuukei no aida ni nihongo no tango wo oboemasu. - During the break, I memorize Japanese words.

休憩のあいだ literally = “the interval of the break” → “during the break”.
あいだ is a noun, so the thing that specifies which interval it is (here, the break) goes before it with の.

This pattern is very common:

授業のあいだ – during class
映画のあいだ – during the movie

Without の (休憩あいだ) is not natural Japanese in this meaning.

What is the role of に after あいだ? Is 休憩のあいだに different from 休憩のあいだ?

The particle に is marking a time when something happens.

休憩のあいだに日本語の単語を覚えます。
→ “I memorize Japanese words during the break.”

Here, 休憩のあいだに is a time expression, like “at 3 o’clock” or “on Monday,” and に is the usual particle for that.

You can sometimes drop に in casual speech:

休憩のあいだ、日本語の単語を覚えます。

This is also understandable and used, but 休憩のあいだに feels a bit clearer and more standard, especially for learners.

Can I say 休憩中に instead of 休憩のあいだに? Are they the same?

They are very close in meaning and often interchangeable:

休憩のあいだに日本語の単語を覚えます。
休憩中に日本語の単語を覚えます。

Both can be understood as “I memorize Japanese words during the break.”

Nuance:

休憩のあいだに – literally, “in the interval of the break”; neutral “during the break.”
休憩中に – “while (I am) on break / in the middle of a break.” This can sound a bit more like “in the period when I’m in break mode.”

You will often see 休憩中 on signs meaning “Closed / On break now.”

For your sentence, both sound natural.

What is the difference between あいだ and あいだに?

The distinction is clearest with verbs, but the idea is:

Vているあいだ – something happens throughout the whole period.
Vているあいだに – something happens at some point within that period (not necessarily continuously).

Examples:

テレビを見ているあいだ、雨が降っていました。
→ While I was watching TV, it was raining (continually during that whole time).
テレビを見ているあいだに、雨が降り出しました。
→ Sometime while I was watching TV, it started to rain.

In your sentence, 覚えます is more like a series of actions within the break, not a continuous state, so あいだに (something that happens in that span) is natural.

With nouns like 休憩, あいだ vs あいだに is less strict, but あいだに is the usual choice when it directly modifies an action.

Why is の used between 日本語 and 単語? What does 日本語の単語 mean exactly?

の again links two nouns:

日本語 – the Japanese language
単語 – a word / vocabulary item

So 日本語の単語 = “words of Japanese” → “Japanese words / Japanese vocabulary items.”

This N1 の N2 pattern is extremely common and often corresponds to English “N1’s N2” or “N2 of N1”:

英語の単語 – English words
フランス語の単語 – French words

So the sentence is about memorizing vocabulary items that belong to the Japanese language.

Could I say 日本語単語 without の?

Normally, no. 日本語単語 sounds unnatural in everyday Japanese.

There are many compound nouns without の (like 日本語教育 “Japanese-language education”), but 日本語単語 is not a common or natural-sounding compound. People say:

日本語の単語
or simply 単語 if the language is clear from context.

So for “Japanese words,” stick with 日本語の単語.

What exactly does 覚えます mean here? Is it “memorize” or “remember”?

The verb 覚える basically means “to learn / commit to memory / memorize.”

日本語の単語を覚えます。
→ “I memorize Japanese words” / “I will memorize Japanese words.”

Important contrasts:

覚える – to learn/memorize something so it enters your memory.
覚えています – “to have it in your memory now” → “I remember it (I know it).”
思い出す – to recall something from memory → “to remember (recall).”

So your sentence is about the act of learning/memorizing, not about recalling something you already know.

Why is the verb in the polite form 覚えます instead of the dictionary form 覚える?

Japanese has different politeness levels.

覚える – plain / dictionary form (casual; used with friends, in internal monologue, in dictionaries, etc.).
覚えます – polite ます-form (used in most everyday conversations with people who are not very close, and in textbooks).

Your sentence:

休憩のあいだに日本語の単語を覚えます。

is in polite style. The casual version would be:

休憩のあいだに日本語の単語を覚える。

Both are grammatically correct; you choose based on the level of politeness you need.

What tense/aspect is 覚えます? Does this sentence mean I always do this, or that I will do it this time?

Japanese non-past (覚えます / 覚える) covers both present and future. Context decides:

Habitual / general rule
- “I (usually) memorize Japanese words during breaks.”
Planned / near future
- “(From now on / today) I will memorize Japanese words during the break.”

Without more context, many people would read this as a habit or personal rule:

“During breaks, I (make a habit of) memorizing Japanese words.”

If you want to clearly show it’s a habit, you can add something like いつも (“always”):

いつも休憩のあいだに日本語の単語を覚えます。

Why is を used after 単語? Could I use は or が instead?

を marks the direct object of a verb:

日本語の単語 – Japanese words (object)
覚えます – memorize (verb)

So 日本語の単語を覚えます means “(I) memorize Japanese words.”

About は and が:

日本語の単語は休憩のあいだに覚えます。
Here は makes 日本語の単語 the topic:
“As for Japanese words, I memorize them during breaks.” (Maybe in contrast to something else.)
が would not replace を here. が generally marks the subject, not the direct object. You might have:
- 私が日本語の単語を覚えます。 – I (as opposed to others) will memorize the Japanese words.

So in your original sentence, を is the correct choice to mark the thing you are memorizing.

Can I move 休憩のあいだに to a different place in the sentence?

Yes. Japanese word order is flexible as long as the particles stay with their words. These are all natural:

休憩のあいだに日本語の単語を覚えます。
日本語の単語を休憩のあいだに覚えます。

Both mean the same thing. The first one slightly emphasizes the time (“During the break, I memorize Japanese words”), while the second focuses first on what you memorize.

You can also say in spoken Japanese (with a slight pause):

日本語の単語を覚えます、休憩のあいだに。

This sounds like adding “— during the break” as an afterthought.

Is 休憩のあいだに日本語の単語を覚えます natural Japanese? How might a native actually say this?

Yes, it is natural and correct. It sounds clear and a bit textbook-like, which is fine.

A native speaker might also say, depending on style and nuance:

休憩中に日本語の単語を覚えます。
休憩時間に日本語の単語を覚えます。
休憩のときに日本語の単語を覚えます。
休憩中に日本語の勉強をします。 – “I study Japanese during breaks.”

Your original version is good Japanese and perfectly understandable.

What does 休憩 literally mean, and how is it different from 休み?

休憩（きゅうけい） – a short break / rest / pause, typically during work, class, or study.
- Example: a 10-minute break between classes.
休み（やすみ） – more general: time off / holiday / day off / break.
It can mean a small break, but also things like:
- 夏休み – summer vacation
- 仕事の休み – days off from work

So:

休憩のあいだに日本語の単語を覚えます。
→ “During (short) breaks, I memorize Japanese words.”

If you said:

休みのあいだに日本語の単語を覚えます。
it might sound more like “During the vacation / during my days off, I memorize Japanese words.”

Why is あいだ written in hiragana here instead of the kanji 間? Is there any difference?

There is no difference in meaning or grammar.

あいだ and 間 are the same word, pronounced あいだ.

Writers often choose hiragana for:

making the sentence easier for beginners, or
making the text look lighter / more readable.

So you could also write:

休憩の間に日本語の単語を覚えます。

Both 休憩のあいだに and 休憩の間に are correct.

How would I say “While I’m on break, I’m memorizing Japanese words right now” (an ongoing action) instead of a general habit?

Use the ～ている form to show an ongoing action:

今、休憩中で、日本語の単語を覚えています。
→ “I’m on break now, and I’m memorizing Japanese words.”

Or more compactly:

今、休憩中に日本語の単語を覚えています。
今、休憩のあいだに日本語の単語を覚えています。

Adding 今 (“now”) plus 覚えています makes it clear this is happening right now, not just as a general habit.

Could I say 休憩のときに instead of 休憩のあいだに? Is there any nuance difference?

Both are possible:

休憩のときに日本語の単語を覚えます。
休憩のあいだに日本語の単語を覚えます。

Nuance:

～のときに – “when / at the time of …”
→ often focuses on the moment or occasion: “When I’m on break, I memorize Japanese words.”
～のあいだに – “during the period of …”
→ emphasizes the span of time: “During the whole break period, (I use that time to) memorize Japanese words.”

In everyday conversation, the difference is subtle, and both will be understood similarly.