Learn Hardcore Japanese: sensei no kotoba ha wakakariyasui desu. - The teacher’s words are easy to understand.

More generally, A の B often means “B that belongs to A / is related to A”.
So 先生の言葉 is “words related to the teacher,” which we usually translate as “the teacher’s words” or “what the teacher says.”

Why is 言葉 (ことば) used here? Could we say 日本語 or 話 instead?

言葉 is a flexible word that can mean:

words
language
way of speaking / expression

In 先生の言葉は分かりやすいです, it has the nuance of “the teacher’s way of expressing things / the things the teacher says.”

You could say:

先生の日本語は分かりやすいです。
→ The teacher’s Japanese is easy to understand.
(Focus is on their Japanese as a language skill.)
先生の話は分かりやすいです。
→ The teacher’s talk/explanations are easy to understand.
(Focus is on their talks/lectures/stories as units.)

先生の言葉 is a bit broader and can cover word choice, phrasing, and general speech.

What is the role of は in 言葉は? Why not が?

は is the topic marker. It roughly means “as for …” or “speaking of …”.

先生の言葉は分かりやすいです。
→ As for the teacher’s words, (they) are easy to understand.

If you used が, you’d get:

先生の言葉が分かりやすいです。

This is grammatically correct, but the nuance shifts:

は: Sets 先生の言葉 as the topic—what you’re talking about in general.
が: Emphasizes 先生の言葉 as the thing that is easy to understand, sometimes in contrast to something else (e.g., other people’s words).

In many neutral statements like this, は is more natural because you’re simply describing the teacher’s words as a topic.

Is 分かりやすい a verb or an adjective? How is it formed?

分かりやすい is an い‑adjective.

It is made from:

分かる = to understand
〜やすい = “easy to do (something)”

So, literally, 分かりやすい means:

“easy to understand”
“easy to be understood”

In grammar terms:

Dictionary form: 分かりやすい
Negative: 分かりやすくない
Past: 分かりやすかった
Adverbial: 分かりやすく (e.g., 分かりやすく説明する = explain in an easy‑to‑understand way)

So in the sentence, it works like a normal adjective:
先生の言葉は分かりやすいです。 → The teacher’s words are easy to understand.

What’s the difference between 分かる and 分かりやすい?

分かる = to understand / to be understood
- 先生の言葉が分かる。
  → I understand the teacher’s words. / The teacher’s words are understood.
分かりやすい = easy to understand
- 先生の言葉は分かりやすい。
  → The teacher’s words are easy to understand.

So:

分かる talks about the actual act/state of understanding.
分かりやすい talks about the inherent ease of understanding something.

You usually use 分かりやすい for describing how clear or accessible something is (books, explanations, teachers, manuals, etc.).

Why does the sentence end with です? Can we say 先生の言葉は分かりやすい without です?

です is the polite sentence ending (copula) in Japanese.

先生の言葉は分かりやすいです。
→ Polite, appropriate for most situations (to a teacher, in class, at work, etc.).

You can say:

先生の言葉は分かりやすい。

This is the plain (casual) form. It’s natural:

when talking with close friends
in informal writing (diary, notes, some internet posts)
in fiction dialogue between familiar characters

So:

Use 分かりやすいです in polite speech.
Use 分かりやすい (without です) in casual/plain style.

Are the spaces between the words (先生　の　言葉　は　分かりやすい　です) normal in Japanese writing?

No. In normal Japanese writing, you do not put spaces between words.

The sentence would usually be written as:

先生の言葉は分かりやすいです。

Spaces are sometimes added in textbooks or teaching materials to help beginners see the word boundaries. But in real Japanese (books, websites, signs, etc.), you should expect:

mixed kanji + kana, no spaces between words.

Can 言葉 here mean “language” as in “The teacher’s language is easy to understand”?

Context matters, but yes, 言葉 can have the nuance of “language / way of speaking”.

In 先生の言葉は分かりやすいです, the most natural interpretations in English are:

The teacher’s words are easy to understand.
What the teacher says is easy to understand.
The teacher’s way of expressing things is easy to understand.

It doesn’t usually mean “the teacher’s mother tongue” or “the teacher’s language (e.g., English, Japanese)”—for that, 日本語, 英語, etc. are clearer.
Here, 言葉 focuses on how the teacher expresses ideas.

Is 分かりやすい always written with the kanji 分, or can I write わかりやすい?

Both are fine:

分かりやすい
わかりやすい

In modern Japanese:

分かる / 分かりやすい are often written partly in kana (わかる, わかりやすい) in everyday texts.
Using 分 adds a slightly more formal or “textbook” feel, and is common in learning materials and more formal writing.

You might also see the old form 分かり易い, but 易 for やすい is less common nowadays.
For everyday purposes, 分かりやすい or わかりやすい are both acceptable and common.

Could I say 先生の説明は分かりやすいです instead? Is the meaning different?

Yes, that’s a very natural sentence:

先生の説明は分かりやすいです。
→ The teacher’s explanations are easy to understand.

Nuance differences:

先生の言葉は分かりやすいです。
→ Focus on the teacher’s words / way of speaking in general.
先生の説明は分かりやすいです。
→ Focus specifically on the teacher’s explanations (how they explain concepts, give lectures, etc.).

Both are correct; which one you choose depends on what exactly you want to emphasize.