First, welcome to Flyertalk miliaxy,

Not certain this is the proper forum for this, but I'll take a stab at the start of an answer. It always does help when we know which airline we are talking about, since the way things work can differ carrier to carrier, and depending on how the ticket was paid for.

Basically PNR is Personal Name Record and is like a web address if you may, a link to where someone's flight information is stored, how they paid, assigned seats, special requests, contact information, flights, etc... More then one person can be on a PNR at a time too...
There are many reasons that PNR's are split, including travel plans changing for one and/or all of the passengers, (have to create a unique six digit code for each person to keep track of the itins then), or an upgrade clears for some but not all people on a reservation. So its basically an accounting way of keeping track of trips for different people, due to changes that are either voluntary or involuntary (reroute due to weather etc and only 1 seat on an aircraft)

There are also some instances where a PNR 'can't' be split, for instance a 2 for 1 ticket special thru a credit card (both passengers must stay on same itin) and sometimes reasons to not split... but I digress

If we had some more information about carriers involved though, we'd be able to explain a little more specifically about what the CS desk was trying to do...