The Nexus is a base for the Combine forces in a city or sector. It is here that the city is operated from. The average Nexus contains many rooms. At the bottom is usually where the prisoners are kept, and at the top is the Administrator's Office. Some Nexus' contain macabre execution chambers, like acid pits or incinerators. Every Sector has a Nexus. They are usually heavily guarded, either by forcefield doors, Combine Locks, Civil Protection Units, or sometimes even Overwatch Transhuman Arm Soldiers. The Nexus must be guarded, because it the center of Combine activity in the City, which is where they live, their equipment is stored, and other VIP members reside (Such as The City Administrator, or Commander) along with prisoners who have been placed in Detainment.
This area is restricted to citizens, unless you are being taken in by a Civil Protection Unit. If you enter without either having permission, to or without a Civil Unit escorting you, you will likely be detained and brought in for questioning, or possibly even shot. It is not recommended to try to break into your city's Nexus as it is considered a high-level violation on most servers.