The statement refers to random walks (colloquially called "drunk walks") in 2 and 3 dimensions respectively. In 2 dimensions, it has been proved, a point will almost surely return to it's starting point, but the probability drops as the dimension increases. In 3 dimensions, the probability drops to somewhere around 34%. 

Of course, if we were aware of the existence of super-beings that could freely traverse 4th dimensional space, we could extend the statement even further as "a drunk man usually finds his way home, and a drunk bird most probably wouldn't be able to. Thankfully super-beings aren't allowed in pubs.

Unfortunately (or fortunately) we cannot crack this joke since we aren't aware of the existence of such super beings. 

(Or are we?)

It's a murder with drunk crows, that's for sure.

More details in this enjoyable blog post here.