A blockchain operates as a single, long chain where all transactions happen. However, this can lead to issues and thus a sidechain off the main one can come in to alleviate problems.
A side chain is essentially another chain or ledger where transactions are recorded, but not on the main chain. This secondary side chain will be linked to the primary blockchain through a two-way link and thus offer some assistance in handling transaction volumes.
Sidechains also come into effect when thinking of the blockchain space as an entire network. With each chain having its own rules and functionalities, there is often difficulty in interoperability between chains. But, having a sidechain means some of these rules can change and become bridges to other blockchains.
Having this interconnected sidechain ecosystem of blockchains would allow for tokens and other digital assets to move back and forth freely from the main chain. Having an interconnected network of blockchains means far more possibility and potential that individual blockchains and their interoperability cannot currently offer.
The benefits of implementing side chains in decentralized networks are huge. For instance, take the gaming industry. Let's say you are playing a popular decentralized Role-Playing Game and your character has just found a unique in-game item that was hidden in a specific world. Your friend has just discovered a new decentralized RPG that he started playing.
Currently, there would be no way to have these items operate across the games, but with side chains in a blockchain-enabled gaming world, you could airdrop that weapon to them and have it operate in-game thanks to side chains.
With regards to scaling, a solution like sharding basically employs side chains as Sharding is considered a layer 1 solution as it is implemented into the base-level protocol of the blockchain. It basically divides the network into teams. After fractionating the network each node is responsible to process its own transactions.