Collateral is a very basic concept in the financial industry, it just means something you put up as a guarantee when borrowing money. If you can't pay back, your collateral will be used to pay your debt. An easy example is when you take a house loan from a bank, the house you bought will be the collateral, if you can't pay back your loan, the bank will take your house.
It is exactly the same in DeFi, if you want to borrow some assets from the protocol, you will need to give the protocol some other assets as collateral, if you don't pay back your loan, the protocol will not give you back your collateral. Since we are talking decentralized finance here, the acceptable collateral are usually crypto-assets.
Since crypto value changes often, it is risky to use crypto as a collateral because when the value of collateral drops, it might not be enough to cover the loan value. For example, let's assume today both BAT and REP are $1 each, I borrowed 1 REP from a lending protocol using my 1 BAT as collateral. Tomorrow, the price of BAT drops to $0.5, but REP is still $1, now if I don't pay my debt, the protocol will end up losing $0.5 as they try to sell my BAT to cover the 1 REP I borrowed.
That's why most protocols requires an over collateralized loan, basically means you can only borrow up to a percentage (less than 100%) of your collateral's value. The protocol often describes this as a loan-to-collateral ratio, and it is a common requirement to control the risk exposure to the protocol. Now when you borrow assets, you can only borrow up to maybe 75% of your collateral value, which will leave a 15% buffer for price changes.
Since price volatility is relatively unique to each asset, is is common to set the loan-to-collateral ratio individually for different asset pairs. For example, Compound calls the loan-to-collateral ratio the Collateral Factor and it is set differently according to different assets.
Liquidation basically means when your collateral price drops closer to your debt value or is even unable to support your debt value, the protocol will allow someone else to repay your debt in exchange for your collateral.
For example, assume the price of 1 REP equals to 1 BAT, you borrowed 1 REP and put 1.5 BAT as collateral because the protocol requires over collateralization. After a while BAT price dropped and now 1.3 BAT = 1 REP. This is risky for the protocol because the protocol might become insolvent if BAT keeps dropping, so the protocol will allow other people to come in and provide 1 REP in exchange for your 1.3 BAT.
Often, the protocol will provide a bonus for liquidators to encourage liquidation in a timely manner, this is usually called a liquidation bonus or liquidation incentive.