When てくる follows a verb of movement or an action, it often means you go somewhere, do that action, and come back. For instance, ちょっと買ってくる means you'll go out to buy something and return. This is very common in everyday speech when you step out briefly.

It can also show that something has been happening or changing from the past up to now. For example, 太ってきた means you have been gaining weight over time. The focus is on the process leading to the present, not just the result.

You'll hear this pattern a lot in casual conversation. It's fine in both speaking and writing, but using it often makes your Japanese sound natural and connected to the speaker's perspective.