Correct, Tarzanboy.
However, crossovers are not brick walls. If your crossover point is 80 hz lowpass, some information will still pass through above that frequency or below if it is highpass. This is where the "slope" comes into play. Basically it determines how quickly the frequecies are rolled off from that point. These are designated by octaves. One octave above 80hz is 160 hz. One octave below 80hz is 40hz.
Most basic crossovers roll off at -12db per octave. So, our sub is crossed over at 80 hz lowpass at -12db per octave. If the output of the sub is 100db at 80hz it would be 88db at 160 hz (or -12db) and 76db at 320hz (or -24db) as it drops off at -12db per octave. If we were to high pass the crossover at the same frequency, same output level, and same slope the main speakers would be -12db down or 88db at 40hz and -24db down or 76db at 20hz. That is of course if they could play that low.
Having a steeper slope can help with integration of speakers in some instances. Especially subwoofers. A steeper slope will allow less upper harmonic/octave information through.
For instance say we use the same crossover point and the same output level, but use a -24db/octave slope. The sub would now be at 76db at 160hz (if at 100db at 80) or -24db, and 52db at 320hz or -48db.
If this is too technical or more than you wanted to know tell me. If you would like more clarification on any of it please tell me.