Many times, companies may not be able to have one or two days downtime to move during the day. Call centers core business is answering phones, they operate 7 days a week, 365 days a year and can't afford any downtime during business hours.
If the building you lease space from allows moving during the night then it can often be the best and cheapest option for your office move. The Movers don't have to deal with other people in the hallways, they can use all or most of the elevators and there's very little traffic on the drives between spaces.
Internet and phone lines should be set up and ready to plug in when the movers install electronics during the night to ensure no problems the following day.
The hourly rate is oftentimes a little bit higher, but the time it saves more than makes up for the cost.