Au printemps, ma tante aime tailler la haie, puis désherber autour des fleurs.

Au printemps is the normal French expression for in spring / in the spring.

French usually says:

• au printemps
• en été
• en automne
• en hiver

So printemps is the exception learners need to memorize. Here, au is the contraction of à + le.

This puts the time setting first: In spring, ...

French often begins a sentence with a time phrase like this:

• Au printemps, ...
• Le matin, ...
• En été, ...

It works very much like English fronting: In spring, my aunt likes...
The comma is also normal here because the time phrase is being set off from the rest of the sentence.

Because tante is a feminine singular noun, so the correct possessive adjective is ma.

French possessive adjectives agree with the noun possessed, not with the owner:

• mon oncle = my uncle
• ma tante = my aunt
• mes cousins = my cousins

A useful extra note: before a feminine noun beginning with a vowel sound, French often uses mon instead of ma for ease of pronunciation:

• mon amie = my female friend

But here tante begins with a consonant, so ma tante is the normal form.

After aimer, French commonly uses an infinitive directly:

• aimer + infinitive

So:

• ma tante aime tailler la haie = my aunt likes trimming the hedge / likes to trim the hedge

French does not need a separate word equivalent to English to here. The infinitive itself, tailler, already carries that idea.

Because aimer is one of the verbs that takes an infinitive directly.

So you say:

• aimer faire
• aimer lire
• aimer jardiner

Not:

• aimer de faire ❌

Some French verbs do need a preposition before an infinitive, but aimer is not one of them.

In a gardening context, tailler means to trim, to prune, or to cut back.

So tailler la haie means:

• to trim the hedge
• to cut back the hedge

It does not mean simply to cut in a general sense. In this context, it suggests shaping and maintaining the hedge.

French uses articles more often than English does.
So where English may say trim hedge only in very limited contexts, French normally says tailler la haie.

Here la haie means the hedge. It refers to the hedge being worked on, probably the one at the aunt’s house or garden.

In French, bare nouns are much less common than in English, so including the article is normal.

Puis means then, after that, or next.

It links the two actions in sequence:

1. tailler la haie
2. désherber autour des fleurs

So the idea is:

• My aunt likes trimming the hedge, then weeding around the flowers.

It is a little more orderly and sequential than a simple and.

Désherber means to weed or to remove weeds.

It comes from herbe = grass/herb/vegetation, with the prefix dés-, which often gives the idea of removing something.

So:

• désherber autour des fleurs means
• to weed around the flowers

It does not mean planting flowers or cutting the flowers themselves. It means removing unwanted growth near them.

Because in French, de + les contracts to des.

The expression is:

• autour de = around

Then:

• de + les fleurs becomes des fleurs

So:

• autour des fleurs = around the flowers

This des is a contraction here, not just the indefinite plural article some.
That is an important point, because des can mean different things depending on context.

Here it most naturally means the flowers, because des comes from de + les after autour de.

So:

• autour des fleurs = around the flowers

This is different from sentences where des is simply the plural indefinite article:

• J’achète des fleurs = I’m buying some flowers

In your sentence, the preposition autour de causes the form des.

Because both verbs depend on aime.

The structure is:

• ma tante aime
  • tailler la haie
• puis
  • désherber autour des fleurs

In English, we might say:

• My aunt likes trimming the hedge and then weeding around the flowers.

French keeps both actions in the infinitive because they are both things she likes doing.

Both are good.

• likes to trim the hedge
• likes trimming the hedge

Both can translate aime tailler la haie.
English often uses either like + infinitive or like + -ing with little difference in meaning here.

So the French structure aime + infinitive can often be translated either way.