What it means
A gripe is a small complaint, a little grumble, that one thing getting under your skin and making you moan about it. If someone asks what your gripe is, they mean what's bothering you. It's common everyday English, especially in the UK, and you can use it as a verb too, so you can gripe about something.
Usage examples
"My only gripe is this car park, it’s rammed, the ticket machine nicked my quid, and now I’m circling like a mug."
"My only gripe with the new cafe is that they play the music far too loud for a Monday."
"She had a quiet gripe about the cold office, then quietly bought everyone a little blanket."
"I've got a small gripe with this flat, the shower's got two moods, arctic misery or lava attack."
"He's always got some gripe about the office coffee, mate drinks it every day anyway."
Where it comes from
Gripe goes back to Old English and is related to the same word family as grip. It first meant to seize or clutch. The complaint sense turned up later, with the idea of something mentally pinching at you and not letting go. That’s why a gripe feels small but clingy.