not too long ago on this very Board. World-Jumper, in the context of misunderstanding a post from hS meant to be humourous, spells out the differences.

But to summarize, Pippa's Ghost is off. The difference beween "alright" and "all right" is in the usage:

When referring to someone's well-being or to say that something is acceptable, use alright:

"Are you alright?"

Q: "How did you do on the test?"
A: "I did alright."

Otherwise, use all right:
"Those cans were all right there! I don't know where they could be now?"

(Speaking to a group of people:) "Your opinions are all right, in their own way, but each one of you has missed a crucial point."

In British usage, it's "all right" if you're using it as an adjective, but "alright" for using it as an adverb.

Or at least it was until a few decades ago. Nowadays the trend is towards using the American-style "all right" for all situations.