Strength is a very important attribute for most gladiators. Almost all weapons have a strength requirement (to equip something in the off hand you need twice the strength requirement) so some points placed in strength is necessary.
Strength increases the damage you deal with weapons. The damage you deal each attack is calculated from the damage of the weapon plus a value that is based on your strength (a bit simplified but that is the basic calculation). So, the more strength you have the more damage you will deal, even if you have the same weapon.
Note: Endless amounts of strength will not help since you can reach the “damage roof” of the weapon. That is the max damage you can deal with an attack with a weapon regardless of how much strength you have.
Strength mitigates the negative effect of your characters total weight which you can read more about here.