Compression test is a effectively a test of how air tight your engine's cylinders are.

As an engine is effectively moving air in compressing it - igniting with a mixture of fuel and then blowing it all out again - the less it leaks the better.

See

http://www.ehow.com/how_5913286_do-compression-test.html

A leak down test is similar but gives you a bit more information about the health of the engine as it helps identify which bit is pants...

See

http://en.wikipedia.org/wiki/Leak-down_tester

This is good advice if everything else fails but first just check the distance you are actually traveling first on those new big tires of yours!

Don't PANIC