The phrase 'deep pockets' means that someone is very wealthy or has a lot of money.
Example in use: One of our partners has deep pockets, we are hoping that his money will help us fund the startup.
In Ireland, this phrase has a different meaning. It is said on wealthy businessman from Tipparary who finished his drink and smash his glass cup on the ground, anticipating that the owner of the pub would ask him to leave the pub.