Specters are AI characters that fight alongside you in Lies of P. You'll be able to strengthen your Specter once you obtain your Wishstone.
My experience has shown that the Specter is more effective when used as a distraction rather than a source of damage. I like to utilize the Indomitable Wishstone and the Friendship Wishstone to prolong its life.
In order to summon a Specter, you require a consumable called a Star Fragment. You can easily buy this item later on and it frequently drops from enemies. So don't worry if you use them frequently;
If you frequently struggle on a boss, even with a Specter, and you don't have a lot of this material then I recommend farming some Ergo and leveling up before using it all, so that you don't have to take on the monster solo if you don't want to.