In Hamlet, what does Polonius mean when he says "brevity is the soul of wit"?

What he's saying, is that, when giving advice or talking intelligently, don't talk too much. In other words, when one attempts to impart knowledge or wisdom, do so in as few words as possible; be brief. Or, to be as pithy as possible: less is more.

Of course, when this precept comes from Polonius, it may be well said, but it's an ironic joke, for Polonius is never ever brief. He presents an excellent adage, which is the complete opposite of what he himself practices. There are few lines spoken by Polonius in the entire play that could not be shortened by at least a half.

The line itself comes from this speech in Act 2, scene 2:

POLONIUS:

This business is well ended.

My liege, and madam, to expostulate

What majesty should be, what duty is,

Why day is day, night night, and time is time.

Were nothing but to waste night, day, and time.

Therefore, since brevity is the soul of wit

And tediousness the limbs and outward flourishes,

I will be brief. Your noble son is mad.

Mad call I it; for, to define true madness,

What is't but to be nothing else but mad?

But let that go.

QUEEN:

More matter, with less art.

Hey, Polonius, the Queen is saying, get to the point already!