Strength is a constant obsession of the world of warriors and demons in Beowulf. Warriors are willing to go to extreme lengths to find opportunities for displaying their physical might, from pointless swimming competitions to ridding another country of the local demon menace. Even the blackest of enemies seems a little more sympathetic in this epic when he (or she) can demonstrate immense physical strength, and even the best of kings or counselors seems a little more pathetic if he can't defeat his foes himself. It's worth pointing out that strength is more important than skill here; skill smacks of deviousness, while strength is simple, straightforward, and pure.
Beowulf's strength is impressive, but it's not his most important characteristic; many of the warriors around him are strong, but, without faith and courage, their strength is useless.
Beowulf's wrestling contest with Grendel is a chance for Beowulf to prove his physical strength; saving the Danes from a marauding demon is just a bonus.