Proof of Work VS Proof of Stake

To put it simply, mining with ASIC miners is POW, and staking (POS) uses wallets with balance to mine; to elaborate further:

In the beginning, proof-of-work was a fantastic innovation that formed the backbone of the original Bitcoin protocol. The idea is that by solving a computationally intensive math problem, one can prove the effort they've put in to secure the protocol. This is how a blockchain is generated, and the effort that is required to perform these computations contributes to a coin's scarcity and value.

However, proof-of-work eventually becomes an extraordinarily expensive system.

Proof of stake solves this issue in a very elegant way. Rather than using computer power as a scarce resource to generate security, Proof of Stake uses the scarcity of the coin itself. A user may choose to "stake" his coins to generate the next block in the chain, and his chance of doing so is basically proportional to the weight of the staked (held) coins.