The best way to explain the multiplier effect is through an example.
Imagine that the government invested £100m in building a new hospital. They would need to employ lots of staff to build and work in the hospital. This would provide extra income to these people and they will spend more in shops.
This will create more demand in the economy. Due to this increse in demand the shops will employ more staff and demand more products from their suppliers. As the suppliers have an increase in demand they will also have to employ more staff.
This increase in employment will create extra income in the economy of which some will be spent in shops. This will cause an increase in demand in the economy and the cycle will repeat again and again.
The investment from the government will cause a circular flow of income and spending. This will cause GDP to increase by more than the initial £100m investment.