One of the definition for 'kouri' is 'to approach' - can you explain how that is? I've tried writing sentences and they don't quite make sense. Mwen kouri nan magazen an--I'm approaching the store?

If you mean I am running towards the store - I'm approaching the store - It makes sense
Unless you're talking about KOURI SOU which mean APPROACHING - running towards, moving towards, drawing near
You can say:
1.
Fanm nan ap kouri sou karantan e l poko vle marye.
The woman is approaching forty and she doesn't want to get married.

2.
M'ap kouri sou de jou depi m pa manje.
I approaching two days since I ate last.
It's been almost two days since I ate.

3.
N'ap kouri sou katrèdtan depi n'ap travay san yon ti kanpo.  An nou fè yon ti poze.
We're approaching fours hours working with a break.  Let's rest a little bit.

4.
Depi konbyen tan remèd ou fini?  M'ap kouri sou de semèn depi l fini.
How long ago did your medication run out?  It's been almost two weeks.

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