I take you want a bit of theory behind it? I'll have a go at making it understandable!
Each NMR active nucleus has what is called an 'Orbital angular momentum' which is denoted I. This is a quantity that comes from some very complex quantum mechanics. These act like small magnets and their interactions determine NMR spectra.
If you have done a bit of physics, you will know about protons and neutrons. Each of these particles has a value of I=1/2, but these can oppose each-other to cancel each-other out. For carbon-12, the main isotope, all the spins cancel so I=0 and is therefore not active. Hydrogen has I=1/2 so is NMR active.
Now in the presence of a magnetic field different orientations of I relative to the magnetic field are different in energy, so there are now two energy states the nucleus can be in. Either opposing or augmenting the magnetic field.
The presence of other magnets, i.e. hydrogens will further split the energy levels. This is easier to explain with diagrams which I don't have, so I'd suggest looking this up.
This develops the n+1 rule. It is important to note that only distinguishable protons will split eachother, (another quantum mechanical phenomenon), which is why the hydrogens in a methyl group do not couple to eachother.