Beacon ETH is the token of Beacon Chain. Beacon Chain will introduce proof-of-stake to Ethereum. This is a new way for you to help keep Ethereum secure. Think of it like a public good that will make Ethereum healthier and earn you more ETH in the process. In practice, it will involve you staking ETH in order to activate validator software. As a validator you'll process transactions and create new blocks in the chain.

Staking and becoming a validator is easier than mining (how the network is currently secured). And it's hoped this will help make Ethereum more secure in the long run. The more people that participate in the network, the more decentralized and safe from attack it will become.