This is a description of why a boomerang comes back. I have tried to make it easy to understand but as accurate as possible.

Going round in a circle

The simplest path a boomerang could take is to fly round in a perfect circle. If you throw a ball it goes "straight", it doen't curve round to one side, but a boomerang does, because a force pulls it round. If you throw a ball tied to a central post (like in a swingball tennis game) it goes round in a circle when you throw it. This is because the string pulls the path of the ball into a curve. The string is pulling in a similar way to the gravity force that pulls the Earth around the Sun. A force that makes something move in a circle is called a centripedal force (lots of people call it centrifugal which isn't really accurate) and it always pulls things in to the centre of the circle.

Force From The Air

The reason a boomerang flies in a circle is because it gets a force by pushing on the air. A boomerang pushes on the air because its arms are shaped in a special way, like the wings of an aeroplane, or a bird.

This shape is called an aerofoil and air that passes over a forward moving aerofoil (e.g.the wing of an aeroplane) gets pushed 'down'.

Lift

When a plane is flying the wing pushes the air down, and because of this the air pushes the wing up. (Imagine sticking your hand out of the window of a car and angling your hand to push the air downwards, you would feel the air pushing your hand up.) This upward push on the wing is called the force of lift even though it isn't always pushing upwards. The lift force could push down if the plane was upside down... risky! Lift is always at a right angle to the motion.

Drag

If you did stick your hand out of the car window you would feel your hand being pushed back by the air aswell as up. This backward push is called drag and slows anything down that is moving through the air. An aeroroil is a shape that gives lift, but hardly any drag, that's why planes use this special shape and not just a flat plank tilted to push the air down.

How Much Force

More lift force from the air pushes on an aerofoil (or a tilted plank) if ...

It goes faster (doubling the speed quadruples the lift force)

It has a bigger area pushing on the air

It is tilted at a larger angle - until the angle gets too big, then decreases. Imagine sticking your hand out of the window and increasing the angle it is tilted at. The lift force (upwards) increases, but after a while it goes away because your hand is flat on to the air.

Unfortunately, the more lift is generated, the more drag is caused too

What Lift does to a Boomerang

The lift on a boomerang does two important things:

1. It keeps the boomerang from falling out of the air, like a plane's wings do.
2. It pushes the boomerang around in a circle.

A boomerang is thrown spinning through the air 'laid over' at about 45 degrees, not 'flat' like a frisby, or a skimmimg stone. Because of this, some of the lift force pushes the boomerang up, and some pushes it side ways so that it has a centripedal force that puhes it round in a circle.

That is how they work, in a nutshell. To keep life simple it is often best to forget gravity for a while, and just think of the lift force pushing the boomerang round in a circle.