From Diablo Wiki
Nephalem Globes (AKA Nephalem Orbs or Power Globes) are yellow glowing orbs that occasionally drop from slain monsters. They look much like Health Orbs (or the purple Progress Orbs found in Greater Rifts), but instead of granting healing (or Greater Rift progress), Nephalem Orbs grant a stack of Nephalem Glory, a bonus that increases Movement Speed and creates arcing bolts of lightning damage.
Normal monsters: chance to drop a health globe on death varies by monster type. Champion monsters: 60% chance to drop a health globe at 50% life and on death. Rare monsters: 100% chance to drop a health globe at 50% life and on death.
Nephalem Glory Buff
The Nephalem Glory can increase up to three stacks, if a player scores three of the orbs in time. Each orb adds a stack and refreshes the buff timer to 60 seconds. (Health Orbs add 5 seconds to the timer, and five health orbs will up the stack one level.) Once a character reaches three stacks, additional Orbs will merely reset the timer to the full duration. If the buff timer runs out, the entire bonus will vanish, instead of simply decreasing by one stack.
- Nephalem Glory – Level 1 - While Nephalem Glory is active, heroes will deal bonus damage with every attack.
- Nephalem Glory – Level 2 - With two levels of Nephalem Glory, heroes will will deal bonus damage that also carries over to nearby enemies with every attack. Additionally, heroes gain 10% bonus movement speed.
- Nephalem Glory – Level 3 - With three levels of Nephalem Glory, heroes will deal bonus damage with every attack that also carries over to nearby enemies. Each hit you land while the buff is active has a chance of creating a damaging explosion.
The bonus damage isn't very obvious, so the movement speed is what most players notice once they earn the second stack.
The overall effect of this buff is not real impactful on gameplay, but it's fun to move faster and see the flashes and streaks of yellow light.