As far as I can see, it changes any input from 0 to 1, kind of like modulo in a way. it takes, say, 7.25, and changes it to 0.25. I guess it's like a [phasor~] if you just cycle up through floats? Am I missing something? What might this object be applied to?

It's mainly used in phase manipulation, but it has many applications. e.g. you can build rough integer rounding for signals by doing
| (input audio)
|\
| [wrap~]
| |
[-~]
| which leaves only the integer part (hypothetically)

it's also used in syncing phasors, for instance to have an oscillator play at 5X the frequency of a master, you do
[phasor~]
|
[*~ 5]
|
[wrap~]

I recently used mmb's approach in http://puredata.hurleur.com/viewtopic.php?pid=14804#p14804 to hard sync an oscillator. it uses samphold~ and wrap~
there are many, many more applications where you'd want to get the fractional part of a signal. see miller puckette's book or the helpfiles for some more examples