There, by analogy with spectral theory, one expects that the regular representation of G will decompose according to some kind of continuous spectrum, of representations involving a continuous parameter, as well as a discrete spectrum.
The discrete series consists of 'atoms' of the unitary dual (points carrying a Plancherel measure > 0).
In the earliest examples studied, the rest (or most) of the unitary dual could be parametrised by starting with a subgroup H of G, simpler but not compact, and building up induced representations using representations of H which were accessible, in the sense of being easy to write down, and involving a parameter.
Then H is chosen to contain AN (which is a non-compact solvable Lie group), being taken as with M the centralizer in K of A.
For the general linear group GL2 over a local field, the dimension of the Jacquet module of a principal series representation is two.