La giacca comprata al mercato è elegante.

Italian usually uses an article where English might not focus on it. La means the and agrees with giacca, which is a feminine singular noun.

• la giacca = the jacket
• una giacca = a jacket

In this sentence, the speaker is talking about a specific jacket, so la is used.

Because comprata agrees with giacca, which is feminine singular.

The base form is the past participle of comprare:

• comprato = bought

But when it is used like an adjective with giacca, it changes:

• masculine singular: comprato
• feminine singular: comprata
• masculine plural: comprati
• feminine plural: comprate

So:

• il cappotto comprato
• la giacca comprata
• le giacche comprate

It is behaving like an adjective phrase attached to giacca.

Literally, comprata is a past participle, but here it describes the noun:

• la giacca comprata al mercato = the jacket bought at the market

This is very common in Italian. It is similar to a shortened relative clause:

• La giacca che è stata comprata al mercato è elegante.

That fuller version is grammatical, but the shorter participle version is much more natural here.

In Italian, descriptive phrases like this commonly come after the noun.

So:

• la giacca comprata al mercato

This is normal word order for a noun followed by extra information that identifies it.

English often does something similar with relative clauses:

• the jacket bought at the market
• the jacket that was bought at the market

Putting comprata before giacca would sound wrong here.

Al is the contraction of a + il.

• a = to, at
• il = the
• al = to the / at the

So:

• al mercato = at the market

Italian regularly combines certain prepositions with definite articles:

• a + il = al
• a + lo = allo
• a + la = alla
• a + i = ai
• a + gli = agli
• a + le = alle

Both al mercato and nel mercato can be possible in some contexts, but they are not always used the same way.

Here, al mercato is the most natural way to say at the market in the sense of bought at the market.

Very roughly:

• al mercato often means at/to the market as a place or activity
• nel mercato more literally means in the market, emphasizing being inside it

So in this sentence, comprata al mercato is the usual phrasing.

È is the third-person singular of essere and means is.

The main structure of the sentence is:

• La giacca ... è elegante.
• The jacket ... is elegant.

So è links the subject (la giacca comprata al mercato) to the description (elegante).

Ha means has, so it would not fit this sentence.

Because it is the predicate adjective, the part that comes after è and describes the subject.

The sentence structure is:

• subject: La giacca comprata al mercato
• verb: è
• complement/adjective: elegante

This is completely normal in Italian:

• Il vestito è bello.
• La casa è grande.
• La giacca comprata al mercato è elegante.

In the singular, elegante stays the same for both masculine and feminine.

• il cappotto è elegante
• la giacca è elegante

In the plural, it becomes eleganti:

• i cappotti sono eleganti
• le giacche sono eleganti

So elegante is an adjective with the common -e / -i pattern.

Yes, but the meaning changes slightly.

• La giacca comprata al mercato è elegante = The jacket bought at the market is elegant
• La giacca che ho comprato al mercato è elegante = The jacket that I bought at the market is elegant

The second sentence adds I as the buyer, because ho comprato means I bought.

The original sentence does not say who bought the jacket. It just describes the jacket as one that was bought at the market.

The main sentence is in the present tense because of è = is.

However, comprata refers to a completed action in the past: the jacket was bought earlier.

So the sentence combines:

• a present description: is elegant
• with a past participle phrase: bought at the market

That is why in English the most natural translation often includes both ideas:

• The jacket bought at the market is elegant.

The article, participle, and sometimes the adjective would change according to gender and number.

Examples:

• Il cappotto comprato al mercato è elegante.
  masculine singular

• Le giacche comprate al mercato sono eleganti.
  feminine plural

• I cappotti comprati al mercato sono eleganti.
  masculine plural

Notice the agreement:

• giacca / comprata
• giacche / comprate
• cappotto / comprato
• cappotti / comprati

And the verb also changes in the plural:

• è = is
• sono = are