A mortgage is a loan to cover the cost of a house. If your house costs £100k, then you need to either have £100k in your bank account or borrow it. If you borrow, it's called a mortgage. A mortgage is long term - typically about 20 years but it varies - and if you fail to keep up with the repayments you can lose your house.
A deposit is money that you have in your bank account. The more money you have, the better your options. You can get a "100% mortgage" which means you borrow 100% of the house value - ie £100k from my example. So you don't necessarily need a deposit, but it helps. Or you can get borrow other amounts if you have the money to use as a deposit. So for a 95% mortgage you'd need to borrow £95k (from the example) and thus would need £5k for the deposit.
Obviously as house prices vary the amount you'd need as a deposit varies too. And there are different lenders who have different criteria, so you will find that if you can put down a larger deposit you have more options.
Typically, you get a mortgage for 3 or 4 times your yearly salary. So if you earn £20k a year you'd get a mortgage for £80k max - so to buy that house you'd need a deposit of £20k.