An ideal is improper if it is the whole thing … whatever thing the ideals are ideals in.
As there are different (but related) kinds of ideal, there are different (but very similar) kinds of improper ideal.
The improper ideal contrasts with proper ideals (all of the other ideals).
The improper ideal does not count as a prime ideal or a maximal ideal, because it is too simple to be simple, although it may satisfy careless or naïve definitions of those concepts (which must be required to be proper).
Conversely, sometimes one defines ‘ideal’ to exclude the improper ideal, but this makes the set of all ideals less nice to work with.