Plasma is a way to create a blockchain (as a set of smart contracts) within a blockchain, by simply committing the root hash of the "meta" child chain (Plasma) on the main chain (Ethereum).
The child chain acts kind of like state channels on steroids, and only the final state transition hash is committed to the main chain. If someone commits an invalid plasma state transition hash/block, the protocol incentivizes committing "fraud proofs", where parties who are interacting in the child chain can show that someone behaved maliciously, and penalize them, reversing the faulty transition.
The child plasma chains can themselves also have child plasma chains, and those chains can have child chains, etc... this "tree" of chains can be reduced through MapReduce, such that billions of transactions/state transitions can be trustlessly/verifiably encoded as a simple hash committment on the root chain.