Analysis is based round the concept of a Resonance – it makes sense, but is difficult to explain. But I will try. Each resonance is associated with one particular atom in your molecule. In theory you might think that it is associated with the particular chemical shift of that atom, but the reason for having the concept of a resonance, is that the chemical shift itself is dependent on many outside influences, such as temperature, pH, salt, ligand etc. This means that any one atom is not associated with any one particular chemical shift. Thus the resonance is there to hold it all together. The reason why you can’t simply use the atom as your central object is that to start with you obviously don’t know which peak corresponds to which atom.
When you pick a peak in Analysis the first thing you have to do to it, is create a new resonance for each dimension. At a later stage you may then add further attributes such as the atom type (Cα or Cβ), or the full assignment, i.e. exactly which atom in the molecule it corresponds to (Asp10Cα or Trp54N). Resonances are numbered from one upwards and are always shown in square brackets in the peak labels and can be looked at and manipulated using the Browse Resonances pop-up which can be called up from the Assignment pull-down menu. The Browse Resonances pop-up is also useful for navigation purposes, as you can mark selected resonances and go to their position within a specified window.
A spin system basically contains all resonances which belong to one amino acid in a protein (or one nucleotide in DNA/RNA or one sugar ring in a carbohydrate). When two resonances are known to be in the same spin system they can be added to a new spin system. Spin systems are initially numbered one upwards and their numbers are shown in curly brackets in the peak labels. Spin systems can be manipulated in the Spin Systems pop-up which is accessed via the Assignment menu. It is possible to associate a spin system with a particular amino acid type and also to merge them (e.g. if resonances originally associated with separate spin systems later turn out to belong to the same one).