A grappler, sometimes referred to a thrower or a wrestler, is a special type of fighting-game character who usually has incredibly poor approach options, but makes up for it by, if they can get in, being able to inflict utterly gigantic damage using highly damaging grabs and throwing attacks. They also tend to have very high flinch resistance, weight or health, poor mobility, and poor range.
Zangief of Street Fighter is the most notable example of this type of character, with characters such as T. Hawk, Alex, Hugo, and Hakan from the same series also signifying the character type.
Up until Super Smash Bros. Clash, the Smash Bros. series has lacked a true grappler-type character. In this game, however, two characters fill the trope, with a past competitior also being modified to play more like one.
Of the three, Bowser is the most like Zangief or Hugo. Bowser is extremely slow, but can pull grabs out at just about anytime. He has by far the worst approach options, and is only slightly more mobile than Black Shadow, but generally has the best close-up between a group of already insane close-up characters. Bowser is known to utterly destroy otherwise poor match-ups if he can get close just once.
Black Shadow is the slowest, but he's best compared to Alex from Street Fighter III and Tatsunoko vs. Capcom. His approach options and mobility are poor, but he is extremely powerful, and is better at setting-up combos not ending in grabs than Bowser is. Black Shadow is extremely scary up close and you should do your best to get away from him.
Knuckles is more comparable to psuedo-grapplers such as Abel from Street Fighter IV when compared to the other two. Knuckles has the best approach options and is the fastest, but is noticeably lighter compared to the other two, has less knockback and damage on his grabs (but both are still extremely high), and is far less dangerous (but he is still extremely dangerous, mind you. Bowser and Black Shadow are just nuts close up.)
It is recommended you go around to look at each of the three's pages for more details on how they play.