I think there are a few things that do this. I am pretty sure there is a gear type that can do that when it's activated that gives bonus dmg on your next attack.
Sap Essence/Power Extraction puts a faint red glow on a nightblade's hands to indicate the major brutality buff is active.
Reaper's Mark puts a red lightning effect on a nightblade's hands for 5 seconds to indicate the increased damage buff.
Leeching strikes puts a black/red glow on a nightblade's weapons while active.
The rally morph of momentum causes a character to glow a faint red.
You are most likely referring to the champion passive "opportunist, which increases your next physical attacks damage after interrupting an enemy. Needless to say for some magicka builds, who very rarely use physical attacks the effect hardly ever gets used up and results in orange glowing hands.
Grim focus causes your weapon to glow a crimson red - the graphic can hang a little after you sheathe your weapon, but I'm not sure if your hands change colour too...
@Sharee and @azhek yes my Khajiit Bowcat gets that all the time I have the opportunist Passive. You do a bash and it comes on. And Razir'Do becomes the Orange glowing kitty of death and wanton Yarn destruction. As long as you bash and Interrupt you get the Glowing paws of death.
There is a 'buff' in East March that will reduce all damage taken player can get if they talk with NPC. Similar to old Grahtwood buff. The hands glow red while the buff is active.
If it wasn't combat related, I think the DK ability igneous shield does this to signal the extra healing done while its up. The glow is more orange-y than red though