Interoperability is an umbrella term that refers to a category of technologies and projects that aim to allow distinct blockchain networks to function together. By design, each blockchain is a closed system, so direct communication between chains is impossible.
The goal of interoperability is to build a continuous financial experience across various networks (such as between Bitcoin and Ethereum), which potentially run on a variety of native assets, consensus mechanisms and token standards. This is of crucial importance if cryptocurrencies are to reach a global scale and be a realistic alternative to traditional finance.
One thing to watch out for in the attempt to make blockchains interoperable is the characteristic of decentralisation. Decentralisation is the very basis of the cryptocurrency movement, and ensures that the problems that plague centralised economic systems today do not carry over to those of tomorrow. In practice, we have to be vigilant if the entities offering interoperability solutions are adhering to keeping their systems decentralised and democratic. It is relatively simple to create systems that allow communication between blockchains and perform well, but run based on the validation of only a few central authorities.