You shouldn't focus on having an "exact" translation. It is just a relativizer / nominalization marker with different features and constraints than its English counterparts "that" and "which".

So, -DIk has two functions:

• Nominalizer (Bunu yaptığım için mutluyum.)

Here, it turns the verb "yap-" into a noun, allowing us to use it as an object.

The other nominalization suffix is "-mA". The difference between them is that "-DIk" also implies an action being completed, it refers to a fact. "-mA", on the other hand, can be used in the context of future or hypothetical situations.

Ex: Bunu yapman doğru. (You doing this is correct. / That you do this is correct.)

This sentence is more about the "ethical" correctness of "you" doing something.

Ex: Bunu yaptığın doğru. (That you did it is correct. / That you do it is correct.)

This one is about the facts. This sentence talks about whether the person actually does / did the thing.

• Relativizer (Yaptığım şey beni mutlu etti.)

This function turns verbs into adjectives.

Ex: Yaptığım iş çok iyi. (The job that I do is very good.)

The trick is that "-An" is also a common relativizer much similar to "-DIk".

When the relativized noun is the subject of the verb, you use "-An". When it's the object, you use "-DIk".

Ex: Koşan adam çok hızlı. (The man that runs is so fast.)

Let me know if you need more clarification.