It can mean a lot of things.

Sometimes it’s just a straight “Hey, you’re doing something
similar, here’s some money to put on your contract along with an
expansion that covers our work too.” In my opinion there’s no
reason for this to be anything other than a simple transfer of your
budget to the other agency, since the other agency should already
have the personnel in place to manage it.

Then you have agencies that exist to provide services to other
agencies. The Naval Research Lab is like this. They have a fund of
tax money they can draw on and they get reimbursed for it by the
requesting agency. Sometimes these agencies will demand a service
charge on top of the cost, other times they’ll detail a dedicated
manager and charge his rates.

Other agencies do what is pretty much straight up money
laundering in my opinion. They charge a service fee as a percentage
of the costs (because it’s totally harder to manage more money) and
sometimes even fees on top of that. NASA charges a “Research Fund”
fee, God only knows what that goes for. I call it money laundering
because those types of fees become slush funds that the servicing
agency can use for anything they want regardless of the original
appropriation.