In the sport of Boxing a southpaw is a fighter who tends to use the "southpaw stance" and, therefore, has his power in his left hand. An orthodox fighter will place his left foot forward, while the southpaw puts his right foot forward. Or, if you have no idea what you are doing, you can fight "squared up" (with no foot forward) and have no power at all. A southpaw fighter does not necesarily have to be "left-handed". If they really like throwing accurate jabs I suppose a right-handed fighter could use the southpaw stance. There are also many fighters who will switch stances during a fight if they think it will give them an edge.
Being a southpaw caries a sort of stigma with it. In Boxing, fighters rely heavily on instinct and rhythm. They get used to how punches are thrown and from what angles they usually come from. A southpaw throws everything backwards. This wouldn't be so much of a problem if there were more southpaws. As it is, it is very hard to find a southpaw to practice against. In general, an orthodox fighter will be at a disadvantage when having to fight a southpaw. The southpaw will have had plenty of experience against orthodox fighters, but not the other way around. It's even a disadvantage for a southpaw to fight a southpaw. Therefore, southpaws often have a hard time getting major fights.
Another problem for an orthodox fighter in facing a southpaw is that the stances clash. The lead feet of the two boxers will be right in front of each other. This tends to cause problems with feet getting stepped on or accidental tripping. There also seems to be more accidental headbutts in this situation.