Operations or "Ops" is the group that coordinates all the activity during the convention, whether that be panels, presentations, or Events, Operations makes it happen. This may include the background activity of building a program, scheduling the speakers (and the rooms), and deconflicting them as necessary to make for a smooth flowing convention.
While Ops is responsible for general coordination, they should generally be the last resort for repairing conflicting schedules; This should have been done in advance by programming staff. Ops does not as much make things happen as keep them happening in order, the way they were planned.
Thin Ops vs Thick Ops
This is also known as the choice between "Small Ops" and "Big Ops" by some conrunners. In the UK there is a division of thought between two approaches to Operations, which are nicknamed "Thin Ops" and "Thick Ops". Basically Thin Ops says that each area is responsible for their own running at the con, and Ops is there to provide the glue to hold the con together, and Thick Ops says that the convention is run by Thick Ops and the various areas provide services that Thick Ops uses to run the convention. In more detail:
Operations is one team of many that make the convention run over the weekend. It may or may not include at-con communications (the radio network(s), pigeon holes for messages etc.) They handle those bits and pieces that don't belong to other departments and perhaps provide a central repository for things like stationery. Thin Ops would assume there is a separate Programme Ops and Green Room team handling finding panelists, getting them drinks, getting rooms reset and that sort of thing; a separate Tech team who will handle all the movement of tech equipment, loading of DVDs etc.; a separate Registration/Members team handling badge problems, membership upgrades etc. a Hotel/Site team handling hotel booking problems etc. Thin Ops is there to handle emergencies, to assist with convention level co-ordination and to receive lost property!
Runs convention on the day. So effectively Programme Ops, Tech Ops, Signage etc. all report into or are handled by the Thick Ops team. Also picks up Logistics (for getting things to and from the Convention), and may be responsible for hiring in any kit required at the con (such as staging, furniture, laser printers, internet access etc.).
Obviously these are two ends of a range, and most cons divide up the Operations work somewhere within that range. So even at a "Thin Ops" convention, you may find Ops handling signage, doing the out of hours membership badges etc. and at a "Thick Ops" convention you might find that Programme, Tech or Art Show are run as very separate teams.