Impleader is a way for one defendant in a lawsuit to bring in additional defendants who may have liability for the plaintiff's claim.
When a defendant impleads someone, they essentially become a plaintiff themselves. They prepare a "third-party" summons and complaint and serve these documents on the new defendant. If the case was originally A v. B and B decided to implead C, the case now becomes A v. B; B v. C. If it's really complicated, with fingers pointing in all directions, there may be multiple "v."'s in the name of the case.
Once the new defendant ("third-party defendant") is impleaded, the original plaintiff has the option of amending their complaint to add the new defendant. If the plaintiff did this in the above example, the case would become A v. B and C.
The claims between the original defendant/third-party plaintiff and third-party defendant are known as "indemnification" and "contribution." Indemnification refers to the shifting of liability because of a contract (e.g. an insurance policy where the insurance company indemnifies the insured) or vicarious liability imposed by law (e.g. respondeat superior, where an employer is liable for certain torts committed by their employees). A claim for contribution concedes some liability, but alleges that the third-party defendant was also partly responsible (e.g. if a building collapses, and both the design and the construction were defective, the contractor may demand contribution from the architect for his share of the total liability owed to the owner).