I understand that describes an action happened a bit before and is catching up to now, but my materials have been nebulous on clarifying that in practical terms. It uses 明日、漫画を持ってくる as example of how it can be used to describe bringing something, 先生を歩いてくる, as one of someone that comes walking, メキシコに行ってきます as one for going and coming back, 雪が降ってくる as one for the snow starting to fall and ワインを買ってくる as one for someone who does something and comes back, but it doesn't clarify those any further than that. Am I missing something?
There are lots of different ways to use -てくる, ranging from physical movement to the flow of time. But they can all be boiled down to 3 main concepts:
- To do something and return.
Knowing the function of the て form, this is pretty straightforward- it is simply connecting a series of sequential events. First, you did something, and then you came (back/here).
I bought the wine and then came (home).
The verb in the て form can even be the complete opposite of くる, and it's still the same thing.
I will go to Mexico and come (back).
- To describe a motion coming towards the speaker.
You could just use くる on its own, but doing it this way allows the speaker to be more descriptive. Were they walking? Running? Flying? You can easily describe how they came, or what they were doing as they were coming.
The teacher is walking (towards me). Or the teacher comes walking.
Tomorrow, I will bring a manga. (I will hold a manga as I am coming.)
- To describe how things have changed or how they will change.
When used in the present tense, -てくる means the action has already started, is still happening, and will continue into the future.
It has (just) started to snow (and it will snow from now into the future).
When used in the past tense, -てきた means the action has happened from the past until now.
It's been getting cold (up until now).
It seems to be a common misunderstanding that ていく always describes a change from now into the future, and てくる does the opposite. This is only true if the former is in the present tense and the latter is in the past. The reality is that if either of them are in the past tense, it means from the past until (no later than) the present, and if they're in the present tense then it means from the present (or before) into the future. (The difference between てくる and ていく in this regard is a separate topic.)