What it means
A cheeky old-school British way of saying someone's swearing nonstop. It usually means they're rattling off a stream of curses because something's gone pear-shaped, but the phrase itself keeps it a bit tongue-in-cheek by hinting at the bad language instead of spelling it out.
Usage examples
"What’s that banging next door? Dave’s trying to put the shed up and he’s effing and blinding every time the drill slips."
"Grandad was effing and blinding at the telly all through the match, Nan had to send him to the shed."
"She came out of the meeting effing and blinding, never seen her that wound up over a spreadsheet."
"You could hear him effing and blinding in the car park when the van wouldn't start again."
"Mum was effing and blinding under her breath after the website wiped the whole booking form."
Where it comes from
A proper British euphemism that showed up by the early 1900s. Effing stands in for fucking, while blinding comes from older minced oaths tied to bloody and blinding. The whole phrase lets people talk about a torrent of swearing without fully spelling the swearing out, which is very British tidy-chaos.