They have 5 albums. In them, Sum 41 has a different sound in each album. Their 2nd album is pop-punk with a little alt metal. Their 3rd album has 2 punk songs amidst melodic hardcore, alt metal, metal, and 2 quiet songs, the band cited Metallica as an influence for this album. (They have also played a full length Master of Puppets cover.) The bands 4th album went back to their roots, stripping the metal influence. This album is pop-punk. Their 5th album is closer to a sequel to their third, with much louder vocals and much better instrumental parts. It is an alt metal/alt rock album with punk influence. Their third and fifth albums also have many shifts from soft to loud within songs. They have songs that include all 4 members on vocals, and utilize a lot of vocal harmony.
Basically, this band isn't groundbreaking most of the time, but they go into a lot of music and pull it off well. Most people write them off due to their first album or think they are copying Metallica, Oasis, Green Day, Blink-182, Linkin Park, etc.