Mol is the abbreviation for mole. 1 mole is 6.02 x 10^23, also called Avogadro's Number after the Italian physicist Amedeo Avogadro. It's a quantity, in the same way that one dozen is 12. To find the number of atoms in 6.02 moles, you multiply it by the number of atoms in a mole:
(6.02 mol)(6.02 x 10^23 atoms/mol) = 3.62 x 10^24 atoms
If you aren't sure whether to multiply or divide by Avogadro's number let the units tell you what to do. Use it as a conversion factor in one of these two forms:
6.02 x 10^23 particles/1 mol, or
1 mol/6.02 x 10^23 particles
If you're starting with moles and want to end up with particles (atoms, molecules, ions) use the first form. Moles will cancel out and your answer will have units of particles.
If you're starting with particles and want to end up with moles, use the second form. Particles will cancel out, leaving moles.