Saving - is putting money aside, bit by bit. You usually save up to pay for something specific, like a holiday, a deposit on a home, or to cover any emergencies that might crop up, like a broken boiler. Saving usually means putting your money into cash products, such as a savings account in a bank or building society.
Investing - is taking some of your money and trying to make it grow by buying things you think will increase in value. For example, you might invest in stocks, property, or shares in a fund.