Hubris is having too much pride and believing you can do no wrong. It is self-confidence run amok.
Odysseus has many reasons to be proud of himself, especially in the context of his warrior culture. He is strong, brave, wily, smart, and overall a good leader. But he brings disaster his way when he gets too cocky.
The most famous example of his hubris is when, having blinded the Cyclops and made his escape, he can't resist shouting out his identity to his injured foe. This allows the god Poseidon to punish him and his crew:
if any man on the face of the earth should ask who blinded you, shamed you so – say Odysseus, raider of cities, he gouged out your eye…
This is a extremely foolish thing to do. The smart move would have to been to get away unidentified, but Odysseus cannot stand the idea that the Cyclops wouldn't know who had bested him. Odysseus just has to have credit for what he did, as if there will be no consequences. It is like having to tell your enemy that you robbed his bank.
And then, still swaggering, Odysseus has the nerve—or hubris—to say to his men:
Did I not keep my nerve, use my wits, to find a way out for us.
Odysseus will learn to be less arrogant, but not yet.