Mr. Incredible's primary superpower is super strength. He is seen bench-pressing locomotives and throwing boulders at speed, even in middle age; presumably his strength was even higher in his prime. This gives him a leaping ability of a few stories, with corresponding agility. He also has good swimming ability, though not as a separate power (he also doesn't hold his breath very well underwater and therefore has to cough for air upon surfacing). His strength also presumably gives him superhuman speed, as he can run significantly faster than a normal human--though not as fast as his son Dash. He's also very agile for a man of his size.
The next most significant power is durability. Mr. Incredible can withstand tremendous amounts of physical trauma, including multistory falls, the direct impact of a train, and breaking through brick walls. He can be cut, though, with very hard metals and a suitable amount of force.
His third and final power is extremely sharp senses. This power is seen when Bomb Voyage is about to blow open the vault of a skyrise building; Mr. Incredible is able to hear the faint beeping of the bomb from the other side of a thick wall.
Mr. Incredible's chief drawback appears to be his ego, especially his vanity and desire to "relive the glory days."
No origin is given for him or his powers, and only very little backstory is told about him. It is presumed that his powers are a birth trait, as with all other explicitly-stated superpowers in the Incredibles Universe.
In the Operation Kronos database, Mr. Incredible was given a threat rating of 9.1, the highest rating of any of the Supers.