When you build an ideal filter, of any type, you usually have two regions: the pass band, and the stop band.
In an ideal filter in the pass band you want a very precise, flat gain, maybe 0dB, while in the stop band you want no gain at all, ideally \$-\infty\$dB.
Now, this is unfortunately not possible in real life. When you build a filter it will have some gain even in the stop band, gain in the pass band will not be flat, and the transition between pass band and stop band can't be infinitely small.
These problems mainly comes from the fact that an ideal filter is not a "nice" function in the f-domain, i.e. it has discontinuities, sharp turns (is this how you call them?) and so on. This needs an infinite time domain response, and this is of course impossible.
Your filter building tool takes care of all these problems by letting you specify all the parameters to build a realistic filter.
Gain is guaranteed to be at most
stop band gain for frequencies below
low end stop and
high end stop, while it is guaranteed to be
pass band gain\$\pm\$half of
pass band ripple for frequencies in the
low end pass..
high end pass interval.
Please note that this is far from being an ideal filter: gain is not flat (it has ripple!) and you have some transition regions between stop band and pass band, and vice versa.
To better understand what is going on, try to input two very near frequencies for low end stop and pass. What happens to the order of the filter? Try to input 0dB as gain in the pass band, and -200dB as gain in the stop band, again, what does the order look like?