Reincarnation is a variant of the iconic Raise Dead spell in Dungeons & Dragons, although it has proven less popular in the wider /tg/ universe than its cousin. Compared to Raise Dead, typically a cleric spell, Reincarnation is a traditionally Druididic spell aimed at bringing dead PCs back to life so you don't need to generate a whole new character. It also tends to be lower leveled and/or cheaper than Raise Dead.
So, why isn't it popular? Well, Reincarnation is a real-life belief that, when you die, your soul is then reborn in an entirely new form. It could be a person of any race or sex, an animal, or a plant. So, Reincarnation the spell puts you at the mercy of the Random Number God, with the potential for "fun" varying widely depending on which edition you're playing. At best, you just wind up an entirely different demihuman or humanoid race to how you started - which could completely fuck over your character class, in some editions. At worst, you could come back as an animal, and thus be unable to play at all... Yeah people tend to stick to Raise Dead for a reason. The sole saving grace of Reincarnate is that the target becomes a young adult and could be someone who died of old age, but this doesn't help it that much. Third Edition limited recipients to the same type (Humanoid ect.), though its still really bad.
Pathfinder would add two new toys that mean it's actually relevant, though still not near its rival. First is Cyclic Reincarnation, which returns the creature in "a body that closely resembles its original body", enough one would mistake them for family, so you won't ruin your build and is manageable. Getting Contingency on the same list as this spell is one of the easier ways to obtain immortality. The second new toy is Forced Reincarnation, a Witch Hex that kills and resurects the target, giving them the negative levels typical of having been brought back to life (and really screwing over dragons). This gives inherent immortality since it can be used on yourself.