Empowering is a full-turn action which allows a mage to consume gems at a lab in return for permanently increasing their abilitiy in a single magic path. To empower to level 1 (from zero) in any path costs 50 corresponding gems: to increase a path's level beyond that costs 15 times the new level.
When empowering in Blood, there is a chance of gaining 1 or 2 of horror marks. For commanders without blood magic, this is 25% to occur; for those with blood magic already it is 7.5% per level of blood they had prior to empowerment. This occurence is mentioned in the empowering message, mentioning that the commander "seems to have attracted the attention of something from the void".
In practice, the high cost makes empowerment something of a last resort for gaining higher magic path access, due to its cost compared to alternatives. These cheaper alternatives are usually some combination of forging magic items which boost paths, and potentially using these boosted paths to summon higher level mages. An additional drawback of any empowered commander is their fragility: compared to items which can mostly be freely removed and transferred between mages, a single empowered mage cannot be separated from their investment. This makes their loss from combat, assassinations, disease, or other causes very undesirable.
In some cases, non-blood empowerment is strategically useful when it allows a mage access to rituals that provide lasting benefit that is otherwise inaccessible. For instance, a nation with only D1 mages will never be able to cast spells beyond D1. Empowering one of those mages to D2 allows you to forge a Skull Staff, boosting that mage to D3; they can then castto make more D3 mages (which can hold the Skull Staff to become D4).
In the rarest cases, it can be worth it to empower a mage that will enter combat, but think very carefully before doing this.
Blood empowerment is more common, simply because blood slaves are worth less than gems. Empowering blood mages high enough to forge blood boosters like, , and is a good way to climb the blood tree. Likewise, empowering nonblood mages in Blood can be a good way to get useful blood crosspaths. Finally, an inefficient but possible way to break into Blood is to mass bloodhunt with scouts until you collect 50 slaves, then empower a commander to B1 and use it to gather more slaves more quickly.
In general, however, most players in most games will never empower even a single time; the dozens of gems required almost always have a better use.