The radioactive spider that bit Peter transferred its characteristics into his 'puny' DNA. Among these was the proportionate strength of a common house spider. His enormous spider-strength allows him to lift or press 10 tons or more (if he's under stress), and perform all kinds of life-saving feats (including lifting buses and shielding little kids from falling debris.) His strength also helps him crash into Four Freedoms Plaza whenever he feels like it.
Spidey's might makes him deadly in hand-to-hand combat, which is his main form of direct attack. He uses strength with his spider-sense and speed in combat, making him extremely hard to surprise, harder to hit, and even harder to withstand. Spidey can go toe-to-toe with a lot of villans in the Marvel universe, and has even held his own against the Hulk from time to time (without the Captain Universe power, even). The greatest advantage of this is...we get to watch him beat the bad-guys silly!
His incredible physical power gives him great endurance, and also helps him take lots of damage. This, coupled with the Parker determination, makes him virtually unstoppable!