Push the boat out
To spend generously. To spend more than one is normally accustomed to doing, often to mark a special occasion.
This phrase originates with the literal meaning, that is, pushing boats from wherever they are beached and into the water. People have for centuries built boats that were too large for an individual to move. Helping a seaman to push the boat out was an act of generosity - a similar to the modern-day act to helping to push a car that is broken down.
The phrase became used in UK nautical circles to mean 'buy a round of drinks' sometime during the 1930s; for example, in J. Curtis' You're in Racket, 1937:
"This bloke you're meeting up the Old Jacket and Vest to-night, let him push the boat out, the bastard. Surely he can pester for a tightener if you're hungry."
The meaning is made clear in Edward Fraser and John Gibbons', Soldier and Sailor Words and Phrases, 1925:
Push the boat out, to, to stand treat.
By 1946, John Irving had listed the term as Royal Navy slang, with the specific 'round of drinks' meaning - in Royal Navalese: a glossary:
"Push the boat out, to, a boatwork term used to imply paying for a 'round of drinks'."
More recently, 'push the boat out' has been used more generally and has come to mean 'behave extravagently; making a purchase that is rather beyond what one can afford'.
See other Nautical Phrases.