A mole is simply a unit of measurement. Units are invented when existing units are inadequate. Chemical reactions often take place at levels where using grams wouldn't make sense, yet using absolute numbers of atoms/molecules/ions would be confusing, too.
Like all units, a mole has to be based on something reproducible. A mole is the quantity of anything that has the same number of particles found in 12.000 grams of carbon-12.
 
That number of particles is Avogadro's Nummber, which is roughly 6.02x1023. A mole of carbon atoms is 6.02x1023 carbon atoms. A mole of chemistry teachers is 6.02x1023 chemistry teachers. It's a lot easier to write the word 'mole' than to write '6.02x1023' anytime you want to refer to a large number of things! Basically, that's why this particular unit was invented.
Why don't we simply stick with units like grams (and nanograms and kilograms, etc.)? The answer is that moles give us a consistent method to convert between atoms/molecules and grams. It's simply a convenient unit to use when performing calculations. Okay... you may not find it too convenient when you are first learning how to use it, but once you become familiar with it, a mole will be as normal a unit as, say, a dozen or a byte