What does the term "Longest chain" mean, as there is only one 'right' blockchain exists? How another longer chain would make the 'right' chain invalid?
Bitcoin's block chain system is really two quite separate systems, and they are easily confused. The first one is the block tree and the second is the active chain.
The block tree consists of all valid blocks whose entire ancestry is known, up to the genesis block. The rules for validness include no double spending, valid signatures, no introduction of more currency than allowed, ... These are the network rules, and every full Bitcoin node verifies them.
The active chain is one path from genesis block at the top to some leaf node at the bottom of the block tree. Every such path is a valid choice, but nodes are expected to pick the one with the most "work" in it they know about (where work is loosely defined as the sum of the difficulties). Relativity and technological constraints prevent us from doing instant communication across the globe, so two nodes can not be expected to pick the same chain as the active one. This is no problem: the mining mechanism makes sure that the chance two nodes disagree about blocks in the past decreases exponentially as they are older.
So no, there is not one "right chain", there are many. Nodes choose for themselves, but the system is designed to make sure consensus arises quickly.
The rules in practice are this: when a new block arrives, and it extends the previous active chain, we just append it to the active chain. If not, it depends on whether the branch it extends now has more work than the currently active branch. If not, we store the block and stop. If it does have more work, we do a so called "reorganisation": deactivating blocks from the old branch, and activating blocks from the new branch.
Imagine that the blockchain is 210000 blocks long and TWO miners both find valid blocks within a few seconds of each other and broadcast them to the network.
This is perfectly normal as the Bitcoin network is peer to peer and global.
You now have two chains, each of length 210001. Neither of these are longer than each other. Some bitcoind nodes will see the first miner's block and some bitcoind nodes will see the second.
Temporarily you have two forks of the blockchain, each of length 210001 blocks long. They are identical for 210000 blocks, but the 210001st is different on the two forks.
Sometime later another miner finds another valid block, the 210002nd block, and that will be attached to exactly one of the forks.
This chain is now the longest at 210002 blocks and becomes the longest chain. It becomes the "definitive" blockchain.
(The transactions in the alternate fork don't disappear - they simply get put back into the pool of unconfirmed transactions and miners will put them into a subsequent block).