What it means
Means having a really good time, the kind where the night properly goes off and everyone's still grinning after. You can say we had a blast after a party, trip, gig, barbecue, whatever turned out stupidly fun. You can also tell someone have a blast before they head out, as a cheeky little wish for a great time.
Usage examples
"After the concert we grabbed late-night food and ended up dancing in the kitchen till 3 a.m. Next day we were wrecked but buzzing. Absolute blast."
"We had an absolute blast at the festival, danced till dawn and lost our voices singing along."
"Have a blast on your trip, send us a postcard from somewhere with a daft name."
"We had a blast at Jamie's barbecue, even after the rain showed up and tried to ruin the vibe."
"You lot have a blast tonight, yeah? Don't do anything too tragic."
Where it comes from
It comes from blast meaning an explosion or a sudden forceful burst. By the early 20th century, English speakers were using it figuratively for a big, noisy rush of fun or excitement. So if you had a blast, the good time didn't just happen, it hit full volume.