יש לי רעיון טוב למתנה ליום ההולדת שלה.

In Hebrew, possession is very often expressed with יש ל־..., literally there is to....

So:

• יש לי = I have
  literally: there is to me
• יש לה = she has
• יש לנו = we have

So יש לי רעיון טוב means I have a good idea.

This is one of the most common Hebrew patterns, and it often replaces a direct verb like to have in English.

לי means to me / for me, and in the pattern יש לי, it gives the meaning I have.

It is made of:

• ל־ = to / for
• י = a suffix meaning me

So:

• לי = to me
• לך = to you (masculine singular)
• לך = to you (feminine singular; same spelling in unpointed text)
• לו = to him
• לה = to her

In this sentence, יש לי literally means there is to me, which English naturally translates as I have.

Hebrew has no separate indefinite article like English a / an.

So:

• רעיון can mean an idea or idea
• רעיון טוב = a good idea

If Hebrew wants to say the idea, it adds ה־:

• הרעיון = the idea
• הרעיון הטוב = the good idea

So the lack of ה־ here tells you it is indefinite: a good idea, not the good idea.

In Hebrew, adjectives usually come after the noun they describe.

So:

• רעיון טוב = a good idea
• literally: idea good

This is the normal order in Hebrew.

A few more examples:

• ספר מעניין = an interesting book
• ילדה קטנה = a small girl
• בית גדול = a big house

Also, the adjective must match the noun in gender and number.
Since רעיון is masculine singular, the adjective is טוב (masculine singular).

Nouns in Hebrew have grammatical gender, and adjectives agree with them.

רעיון is a masculine singular noun, so the adjective must also be masculine singular:

• רעיון טוב = masculine singular
• if it were a feminine noun, you would usually see טובה

For example:

• מתנה טובה = a good gift
  because מתנה is feminine
• רעיון טוב = a good idea
  because רעיון is masculine

You often have to learn the gender of each noun as part of the word.

Here למתנה means something like for a gift or as a gift.

The prefix ל־ often means to, but it can also mean:

• for
• as
• for the purpose of

So in this sentence:

• רעיון טוב למתנה = a good idea for a gift

It does not mean physically moving something to a gift.
Instead, it means the idea is suitable as a gift.

That part means for her birthday.

It breaks down like this:

• ל־ = for
• יום ההולדת = the birthday
• שלה = hers / her

So:

• ליום ההולדת שלה = for her birthday

A more literal breakdown is:

• יום = day
• הולדת = birth
• יום הולדת = birthday
• יום ההולדת שלה = her birthday

In natural English, we simply say for her birthday.

This is because of a Hebrew structure called a construct chain.

The basic expression for birthday is:

• יום הולדת = birthday
  literally: day of birth

When the phrase becomes definite, Hebrew usually marks definiteness on the second noun in the chain:

• יום ההולדת = the birthday

Then:

• יום ההולדת שלה = her birthday

Because her birthday is definite, the Hebrew phrase is also definite.

This can feel strange to English speakers, because English uses her without needing the, but Hebrew often marks possession in a way that makes the whole phrase definite.

In Hebrew, possessive words like my, your, her are often expressed with a separate word placed after the noun:

• שלי = my / mine
• שלך = your / yours
• שלה = her / hers

So:

• יום ההולדת שלה = literally the birthday of hers
• natural English: her birthday

This is a very common Hebrew pattern.

Compare:

• הספר שלי = my book
• החברה שלו = his friend / his girlfriend (depending on context)

So yes, unlike English, the possession often comes after the noun.

שלה is the form meaning hers / her.

The של־ forms change depending on the possessor:

• שלי = my / mine
• שלך = your / yours (masculine singular)
• שלך = your / yours (feminine singular; same spelling in unpointed text)
• שלו = his
• שלה = her
• שלנו = our
• שלהם / שלהן = their

So יום ההולדת שלה specifically means her birthday.

Yes, that is a very literal breakdown, and it is actually useful for understanding the grammar.

A word-by-word style breakdown would be:

• יש = there is
• לי = to me
• רעיון = idea
• טוב = good
• למתנה = for a gift / as a gift
• ליום ההולדת שלה = for her birthday

But that is not how natural English says it.
Natural English is:

I have a good idea for a gift for her birthday.

Literal translation is helpful for learning structure, but you should not aim to sound literal in English.

Yes. In context, that whole phrase means the idea is for a gift intended for her birthday.

So the sentence naturally means:

• I have a good idea for a present for her birthday.

Hebrew often uses stacked ל־ phrases like this:

• רעיון למתנה = an idea for a gift
• מתנה ליום ההולדת שלה = a gift for her birthday

So the sentence builds naturally from one phrase to the next.

Yes, there are other natural ways to say something very similar. For example:

• יש לי רעיון טוב למתנת יום ההולדת שלה.
  = I have a good idea for her birthday gift.

This version uses מתנת יום ההולדת שלה = her birthday gift.

The original sentence is completely natural, though, and may sound a bit more conversational because it builds the meaning step by step:

• a good idea
• for a gift
• for her birthday

So learners should definitely recognize the original as normal Hebrew.

You would only change the possessive at the end:

• יש לי רעיון טוב למתנה ליום ההולדת שלו.
  = I have a good idea for a gift for his birthday.

• יש לי רעיון טוב למתנה ליום ההולדת שלי.
  = I have a good idea for a gift for my birthday.

• ...ליום ההולדת שלנו
  = ...for our birthday / birthday celebration

So the overall structure stays the same; only the final possessive word changes.