At some point, you're going to come across sentences that use the forms um...zu or damit. They are called final clauses (Finalsätze).
We use these clauses whenever we are talking about reaching a certain goal. Sentences using um...zu and damit aim to answer questions about the purpose of something; why we are doing it.
There are two options that you should differentiate between and be aware of:
Option 1:
In this case, there is a choice. We can use both the um...zu and the damit forms. The only thing that changes is how they are used.
Let's take a closer look.
a) um ... zu
Sofia fährt in den Urlaub, um sich zu erholen.
Sofia goes on holiday to recover (herself).
This is an infinitive construction (Infinitivkonstruktion):
1.There is no subject in the subordinate clause → the subject in the subordinate clause is the same as in the main clause (Sofia).
2. The verb in the subordinate clause is in infinitive and at the end of the clause → zu + sich erholen (in infinitive).
b) damit
Sofia fährt in den Urlaub, damit sie sich erholt.
Sofia goes on holiday to recover (herself).
In this case we have the conjunction damit and a subordinate clause with the verb conjugated at the end.
1. There is a subject in the subordinate clause → Sofia, sie
2. The verb in the subordinate clause is conjugated → sich erholt
Option 2:
Sofia fährt in Urlaub, damit ihre Sprachkenntnisse besser werden.
Sofia goes on holiday so that her language skills improve.
Sofia fährt in Urlaub, damit ihre Tochter ein neues Land kennen lernt.
Sofia goes on holiday so that her daughter gets to know a new country
1. The verb in the subordinate clause depends on the subject of the subordinate clause→ werden (3. Person Plural), lernt (3. Person Singular) To get better (3rd person plural), gets to know*(3rd person singular)
2. The main and subordinate clauses have different subjects → Sofia, ihre Sprachkenntnisse/ihre Tochter (Sofia, her language skills / her daughter)
In this case we can only(!) use damit, ie the version with the subordinate clause and the conjugated verb at the end..
When the subject is the same, we can use um...zu or damit. However, when there are two different subjects, we can only (!) use damit.
Subordinate final clauses (Finalsätze) are useful to define a goal, an objective. Have you already reached your goal learning German? :)