Yes it means tired out, worn out, in an exhausted by work/busy day/long walk/exertion sense rather than just plain old tired and sleepy.
It is very informal and considered a bit vulgar. I use freely with friends and family and a few close colleagues, but I wouldn't say it to my boss! Not exactly swearing, but not exactly polite either.
What makes the word vulgar is that "knackers" is a slang term for testicles, which makes it slightly odd when a female person says that she is knackered!
However, the word derives from the horse world, as a knacker is an old, tired-out horse that is put down and turned into glue in a knacker's yard. That is where the connection lies between "I'm knackered" and exhaustion.
'Knackers' was originally applied (I believe) to percussive instruments made out of bone or wood, such as castanets. It's from these that the 'testicular' application derives.
A 'knacker' is also the person who runs the horse-slaughtering business.