Bolt and Bolt Carrier
The piece with the most moving parts is the bolt and bolt carrier. The bolt carrier assembly is located in the upper receiver of the rifle and held in place by the charging handle. The bolt itself is contained in the bolt carrier. Both these parts should be carefully disassembled, cleaned with solvent and well-lubricated with quality gun oil.
Lower Receiver
The lower receiver of the AR-15 contains the trigger assembly and the weapons safety switch. When disassembling your rifle for cleaning is not necessary to further breakdown the lower receiver. However the lower receiver consists of a number of moving parts that need to be lubricated. The interior should be cleaned with a solvent and have gun oil applied.
Buffer Spring
The buffer and buffer spring are housed in the stock and compensate for the recoil of the weapon -- which is why the weapon has virtually no kick. The parts should be removed from the stock and lubricated while you're cleaning your weapon.