What would I be doing if I pushed the boat out?
Going sailing, you might guess.
Of course, that would be far too logical.
We're having a party and we've decided to push the boat out!
Still no sailing involved. It means we're going to spend a lot of money and make a lot of effort. This idiom is usually used with a celebration of some kind.
Now if you really want to push the boat out when it comes to English, why not try and listen to a bit of Geordie? This is the accent of Newcastle and is difficult even for the average Brit to understand!
Here's part of a classic TV series from the 70's - When the boat comes in. Good luck!