Glory Points are used to increase Heroes stats. You must fuse the same hero (good, rare, and epic) to increase the glory points. Epic heroes can increase their glory points up to level 12. For example if you take a level 60 savage chief and fuse a weaker level 1 savage chief to it that is one glory point which is a major stat boost. It is recommended you use duplicate epic heroes for glory points until you fill them up.  You can also use the duplicate epic heroes for Hero Aid. 

I'm not sure what the exact boost is but I have tried it a few times and it seems to be about a 15% HP boost and 25% ATK boost for a single glory point (epic hero) and an additional 10% HP and 10% ATK boost for the 2nd.