Imperil reduces the PMI, MMI, and Elemental Mitigations of monsters. It starts at 25% reduction. It's subtractive, not multiplicative, so a mob with 30% PMI would go to 5% PMI. The upgrade tracks for it improve the mitigation reduction (Better Imperil) and make it hit more targets and improve CD (Faster Imperil). Holy Imperil and Dark Imperil add reductions to Holy/Dark mitigation, respectively.
All mages want Imperil, it's our best debuff since it greatly increases the amount of damage we do.
Melees sometimes use it. If you use a Rapier or Estoc, you most likely do not need Imperil since the Penetrated Armor proc gives you the PMI part (which is what you care about) for free. If you do not use a weapon that procs PA, and you are not 2H or Niten (for Rending Blow or Skyward Sword to proc PA via skills), Imperil can be useful to you as a substitute, especially if your weapon has Fire/Cold/Elec/Wind strike.
However, monster PMI only becomes noticeable once monsters get significant stats and Chaos upgrades. At level 127, high end mobs is probably packing about 30-35% PMI at high difficulties (at low it may be much lower). In that case, Imperil for -25 or -30 is about a 30-40% damage boost on a single target, which may well not be worth it to you unless it saves you a Cure. At my level (282), PMI/MMI values in the 50s or 60s are common among high-end mobs, so 3x stacks of PA or an Imperil (upgraded to 40%) will increase my damage by a factor of 2 or more on high end mobs. That will reliably save significant time and MP (between buff time used and Cures and offensive spells that aren't needed).
QUOTE(Maximum_Joe @ Jul 9 2013, 14:32)

Read the Wiki
Wiki will tell you what Imperil does, but not why you'd want to use it (and when you'd want to start). I also don't know why you assume base Elemental mitigation reduction is 10%, since it was 25% before, level 1 of the upgrade is to 30% and every upgrade is +5%. I'm pretty sure it's going to stay 25/25 unimproved.
This post has been edited by PK678353: Jul 9 2013, 21:53