The purpose of bands worn on football player's arms is to collect or wipe away sweat, similar to a wristband. It has recently become a trend, and many players admit to wearing them as a fashion statement instead of for a functional purpose.
The trend emerged as wristbands began being worn higher and higher on the arm. Players started wearing them above the elbow over the bicep and triceps. Athletic trainers have confirmed that the bands serve no direct purpose from a medical or performance perspective; in spite of this, the NFL has encouraged the wearing of these bands because they display the NFL logo.