A siphon works partly on the same principle as a drinking straw: a difference in pressure.
The atmosphere exerts a pressure on everything on Earth. This is because air is pulled down by gravity in the same way we are.
When you suck on a straw, you decrease the air pressure in the straw and the liquid is pushed up into the straw by the difference in pressure between the inside and outside of the straw.
A siphon can be explained in the same way.
To start the flow of liquid you suck on one end of a tube (just like a straw) and, just like a straw, the liquid is pushed into the tube by the difference in pressure.
Once the tube is filled, the exit end of the tube must be placed at a lower level than the liquid you are trying to siphon. The liquid in the exit side of the tube is then pulled down by gravity, creating a vacuum in the tube.