With POS coins you are staking coins i.e. holding coins in a full node client wallet to accumulate enough stake to mine a block and earn a reward based on the POS annual percentage rate for that coin. Typically with POS you can hold any number of coins and still be eligible to stake. The more coins you have and the longer you have them staking, the quicker you will be able to earn enough stake to mine a block and earn a POS payment. Your client node doesn't need to be online to earn stake, but it must be online to be able to mine a block to earn a reward.
Ethereum will be switching to a hybrid POS/POW system with the Constantinople hard fork expected early next year and it's expected to switch to fully POS in the Metropolis release by the end of next year. That means you won't be able to mine ETH with GPU's after that and instead you will need to hold a number of coins to stake and generate new ETH as interest on the coins you hold.
Hey, the way I understood it they postponed the hybrid transition for at least another year. So 3+ years until masternode system, you will still be able to mine, just the rewards will get split if they choose Casper. If they don't the alternative is 5 years away.
Listen to Vlad Zamfir talk, he's a super nice guy.