Amedeo Avogadro is best known for a number that he did not find. This number, called Avogardo's number, is the number of particles in a mole. Avogadro not only didn't find the number, he never proposed a way to find it or even suggested that it existed. The question thus raised is...why is the number named after him?
Avogadro's hypothesis was simply that equal volumes of gases at the same temperature and pressure contain the same number of particles. In simpler terms, if you had a balloon of hydrogen and a balloon of the same size filled with oxygen in the same room at the same time (so that their temperatures and pressures were equal) they would both contain the same number of particles.
This may not seem earth shaking to you, but at the time it was a huge leap. It suggested, for the first time, that macroscopic measurements could be related to microscopic particles. Thus, knowing that water is made of one oxygen and two hydrogens we could get a liter of oxygen gas and two liters of hydrogen gas and they would combine perfectly down to the atom.
It was this idea, that it was possible to relate the number of particles to macroscopic measurements that set the chemistry world on fire and it is in repspect of that idea that the number is named after him.
Of course, stating that certain volumes of gas have the same number of particles, couldn't help but make people wonder how many particle that was...that led to the mole.