Sidechains are blockchains which handle assets off of the main blockchain and are able to return them to the main blockchain at a future date.
As you understand by now, blockchains are comprised of interconnected computers serving as nodes in a decentralized consensus network. Everything that happens to assets on that blockchain is validated and recorded on that blockchain. If assets are taken to another chain, however, where different protocols may apply to suit the needs of the parties using the assets, this may be called a sidechain.
The assets are able to be returned to their original blockchain at any point as if they were buried in the backyard and one day were dug up and put back into circulation. In reality, the activity in sidechains is anything but sedentary. Market makers and arbitrageurs can use sidechains to find the best prices for their currencies, trading bots clicking and whirring away ceaselessly while the main blockchain records only the tick...tick...tick of the brief moments when the asset reappears on the surface.
Blockstream’s protocol, Liquid, was the first official sidechain technology, launched in 2015 but still in beta at the time of this writing. Its purpose is primarily to offer a sidechain to the major cryptocurrency exchanges. Several others continue to develop solutions for different environments where sidechains appear to be needed. Some, such as Drivechain, use sidechains as a platform for experimentation and study without affecting the primary blockchain, like silent forks that don’t exist except to those on the sidechain.
Currently, the buzz around sidechains is generally in reference to Bitcoin itself. Institutions such as banks that have become comfortable with the longevity of Bitcoin are looking for ways to use it in their own private blockchains. One company working to facilitate that functionality is Multichain. Other platforms, such as Ethereum and Ripple, are already flexible enough to interface between different blockchains. Many sidechains use Ethereum code to create a Bitcoin sidechain. Ripple is already gaining a lot of traction in the banking world because it has never tried to be the One Answer, in terms of the “best” cryptocurrency, but it is developed to be an interledger protocol that can make all currencies and transactions faster and more liquid.
The problem with Bitcoin so far has been speed and scalability (and the pesky mining centralization issue due to ASIC machines). The Lightning Network is a possible solution which has been used successfully in tests by Litecoin, but it is a slightly different animal than sidechains since it would still be public and open while sidechains are normally permissioned. Sidechains are mainly being developed for corporate clients.