When exactly does a monopod come into play. I have never used one and I'm trying to understand the benefits over a tripod.

Moved from Open DV to Monopods.

lots of times to use one. It's flexible meaning easily movable, you can get high shots, dutch angle shots, able to hold a longer shot with pretty good stability, not as good as a tripod but it is certainly better than going strictly handheld.
Now having said all of that, I can only repeat what I always tell people. Tripods, monopods, shoulder brackets, steadicams...anything of that sort are tools of the trade and while a monopod can replace a tripod in certain situations it is best to use the right tool or the job. I've had jobs over the years that have required the use of a tripod and a monopod and a shoulder bracket (I use the DVMultirig after trying many others) and while I COULD have done the job with just a tripod the monopod and DVMultirig made the job more comfortable and allowed me to aquire better footage.
Different tools for the job. A mechanic has more than 1 wrench :-)
Of course a lot depends on the type of work you might be doing as well.