הכוונה שלי הייתה להגיע בזמן, ובסוף באמת הגעתי מוקדם.

הכוונה literally means the intention / the meaning / the idea depending on context.

So הכוונה שלי can mean:

• my intention
• what I meant
• my point

In this sentence, it means my intention:

הכוונה שלי הייתה להגיע בזמן = My intention was to arrive on time

So even though כוונה can sometimes relate to meaning, here it is clearly about what the speaker planned or meant to do.

Because כוונה is a feminine singular noun, and in Hebrew the past form of to be agrees with it.

• masculine singular: היה
• feminine singular: הייתה

So:

• הרעיון שלי היה... = My idea was...
  because רעיון is masculine
• הכוונה שלי הייתה... = My intention was...
  because כוונה is feminine

That is why הייתה is required here.

In Modern Hebrew, possession is very often expressed with של + a pronoun:

• שלי = mine / my
• שלך = your
• שלו = his
• שלה = her

So הכוונה שלי is the normal way to say my intention.

Hebrew does have some possessive endings in certain words and older/literary styles, but for a noun like כוונה, using שלי is the standard everyday pattern.

להגיע is the infinitive, meaning to arrive.

Hebrew often uses the structure:

[noun] + היה/הייתה + infinitive

to express something like:

• the plan was to...
• the intention was to...
• the goal was to...

So:

הכוונה שלי הייתה להגיע בזמן
literally: My intention was to arrive on time

This is very natural Hebrew.

Yes, absolutely.

התכוונתי להגיע בזמן means I intended to arrive on time.

That version is more direct and verb-based.
The original sentence uses a noun:

• התכוונתי להגיע בזמן = I intended to arrive on time
• הכוונה שלי הייתה להגיע בזמן = My intention was to arrive on time

Both are correct. The version with הכוונה שלי can sound a bit more reflective or explanatory, as if the speaker is clarifying what their intention was.

Here, בזמן means on time.

So:

• להגיע בזמן = to arrive on time
• להגיע מוקדם = to arrive early
• להגיע באיחור = to arrive late

In English, on time usually means not late, and that is exactly the idea here.

Sometimes בזמן can overlap a little with in time depending on context, but with arrive, on time is the best translation.

ובסוף literally looks like and at the end, but in natural usage it often means:

• and in the end
• and eventually
• and after all
• and as it turned out

So in this sentence:

ובסוף באמת הגעתי מוקדם
means something like:
and in the end I actually arrived early

It does not mean the speaker arrived at the physical end of something. It is about the final outcome.

Both are possible, but in this sentence actually is probably the best feel.

באמת can mean:

• really
• truly
• actually

Here it adds emphasis and a slight sense of surprise or contrast:

ובסוף באמת הגעתי מוקדם
= and in the end I actually did arrive early

So the speaker is saying something like:
I only meant to be on time, but as it turned out, I really/actually got there early.

Because the verb itself already tells you the subject.

הגעתי means I arrived.
The ending -תי marks first person singular in the past tense.

So Hebrew often leaves out the subject pronoun when it is clear from the verb:

• הגעתי = I arrived
• הגעת = you arrived (depending on gender/context)
• הגענו = we arrived

You could say אני הגעתי if you want extra emphasis, but it is not necessary here.

Because מוקדם works naturally as an adverb-like word here, just like early in English.

So:

• הגעתי מוקדם = I arrived early
• הגעתי מאוחר = I arrived late
  though באיחור is also very common for late

Hebrew does not need an extra word like to or at here.
The pattern is simply:

verb of arriving/moving + מוקדם

The sentence breaks down like this:

הכוונה שלי הייתה להגיע בזמן, ובסוף באמת הגעתי מוקדם.

Part 1:

• הכוונה שלי = my intention
• הייתה = was
• להגיע בזמן = to arrive on time

Part 2:

• ובסוף = and in the end
• באמת = actually / really
• הגעתי = I arrived
• מוקדם = early

So the structure is very close to English:

My intention was to arrive on time, and in the end I actually arrived early.

The main difference learners often notice is that Hebrew does not need I before הגעתי, because the verb already includes it.