What it means
Plastered means completely drunk, not just a bit tipsy. Properly gone. You're swaying, slurring, chatting total nonsense with full confidence, and treating your chips like a complicated life event. It's a really common British and Irish way to say someone got seriously smashed on a night out.
Usage examples
"At the office do she got plastered, tried flirting with the photocopier, then asked Dave from Accounts where the loo was, cradling a plant."
"He got absolutely plastered at the reception and fell asleep under the cake table."
"We were only meant to have two pints, but by midnight Connor was absolutely plastered and trying to order chips from the cash machine."
"She turned up plastered, called the cat mate, then sat on the floor eating garlic bread like it was a spiritual reset."
"By half eleven he was plastered, hugging the kebab shop wall and telling everyone the bouncer was his cousin."
Where it comes from
It comes from the older meaning of plastered as covered or spread over with plaster. By the early 1900s it had shifted into drunk slang, with the idea that booze had hit you so hard you were coated in it, flattened by it, and moving through the night all wonky.