This idiom or expression like phrase means:

Advantage.

When someone says: We have the upper hand in the negotiation, they mean something like:

We have an advantage over them.
We’re in a better position than them.

Q. Do you want to negotiate with Richard?
A. Not really. I have the upper hand here.

This idiom or expression has to do with a couple of things:

Lacking objectivity, as in:
There’s been a lot of hand holding around here. They’re letting their friendship affect their decisions.

Providing support, as in:
This is her first time away from home. She may need some hand holding.

This idiom or expression has to do with:

Helping.
Helping out.

The earthquake victims need a helping hand. Please help them before it’s too late.

This idiom or expression has to do with:

Hitting with the back of the hand.
Returning a shot with the back of the hand.

Also:
She threw him the back of her hand.

He/she steals things.