The substitution effect is when prices rise and people begin buying cheaper alternatives to expensive goods.
For instance if a restaurant sells hamburgers and hotdogs, and increases the price of hamburgers while other variables remain constant, customers will begin buying more hotdogs.
The substitution effect and the income effect come hand in hand. The income effect describes how people will spend more (demanding more goods and services) if their income increases, if other variables stay constant. These two are connected because price changes can trigger also trigger the income effect: if prices of goods increase, then you feel poorer (even if your paycheck is the same), which makes you spend less.