“I was wondering, is there any way that we could move these meetings up earlier in the morning?”
You have a meeting each morning at work. The meeting happens in the middle of the morning. It's not a good time because it interrupts your work. You ask your boss about changing the meeting time.
I was wondering, is there any way that we could move these meetings up earlier in the morning?
This is a way to introduce a request. It makes the question sound really polite:
Hey Jen, I was wondering if I could borrow your textbook over the weekend.
I was wondering if you'd like to go out for coffee some time.
You say "I was wondering if..." even if you're still thinking about this question now. There's no grammatical reason for using the past tense ("was wondering"). That's just how the expression is said.
To "move up" something means to make it earlier. You can "move up" something like a meeting or appointment.
Can we move our meeting up to 1:30?
This is a polite way to ask for something:
Is there any way that you could pick the kids up after school today?
Professor Donovan, I was wondering, is there any way that I could have a couple of extra days to work on my essay?