Cartesian Diver

Cartesian divers  are used to demonstrate the effects of air pressure. 

I used an eye dropper filled part way with water for my diver.  I put colored water in the eye dropper - I think it makes it easier to see what's happening.

Fill a large, plastic bottle with water.  Place the diver in the bottle - the diver should float at this point, make any adjustments you need to to make sure that happens.

Put the cap on the bottle.

Squeeze the bottle and watch the diver dive! 

Why does it dive?

When you squeeze the bottle, you compress the air molecules that are trapped in the bottle, including those inside the eye dropper.  When that air is compressed, additional water enters the dropper (since there's room available).  The additional water (and decreased volume of air) changes the density of the dropper enough to cause the dropper to sink to the bottome of the bottle.

When you release the sides of the bottle, the air trapped in the dropper expands, pushing out the extra water and decreasing the density so the dropper rises. 

A Cartesian diver can be used to explain all kinds of things, like how submarines work, how fish swim bladders work, etc.
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You can also use ketchup (or other condiment) packs as Cartesian divers.  In that case, water doesn't enter the packet, it dives strictly because of the change in density due to the compression of air molecules.