What does "though" mean here?

He tired easily, though he was unable to sleep well at night.
For the sentence above, I fail to see any relation of transition between the first clause and the second clause. Any one could explain to me?

It means "but" or "yet". It implies contrast between the clauses.

The relation between the clauses is because you would expect someone who is tired to sleep, yet this individual doesn't. You could write it like this: "Even though he easily became tired, he was unable to sleep well at night."

I used to have that problem -- exhausted by 8 pm, but tossed and turned all night. Turned out to be a lousy, second-rate thyroid. ;)

Josh Lalonde's reply makes sense to me. Thanks!