A Potentially Visible Set (or Potential Visibility Set) is a collection of visleaves which might be visible from a given location. It is not a precise measure of visibility but thanks to being pre-compiled into a map is a very fast one. It forms the basis for many run-time tests, including networking filtering and rendering control.
See Visibility optimization for in-depth discussion of how leaves and the PVS work.
Console commands

r_novis  <boolean>
Disables the PVS system, causing the whole world to be rendered at once.
r_lockpvs  <boolean>
Prevents the PVS system from updating. Allows direct inspection "behind the scenes".
mat_wireframe  <choices>
While not strictly PVS-related, wireframe mode does allow you to see leaves popping in and out of view.
sv_strict_notarget  <boolean>
If set, notarget will cause entities to never think they are in the PVS.
test_randomizeinpvs  <void>
To do
Programming

Clusters
To do: Difference between a cluster and a leaf.
int engine->GetClusterForOrigin( Vector origin )
Gets the cluster for the given origin.
int engine->GetClusterCount()
The number of clusters in the map.
Tip:ceil(engine->GetClusterCount() / 8.0f) returns the appropriate length for a PVS buffer in the current map.
int engine->GetAllClusterBounds( bbox_t *pBBoxList, int maxBBox )
Gets a list of all clusters' bounds. Returns total number of clusters. bbox_t is a struct containing a min and max Vector.
PVS
A PVS is stored in a byte buffer in which each bit represents the visibility of a cluster.
Bug: Testing an empty PVS can have unreliable results in some situations.
int engine->GetPVSForCluster( int cluster, int outputpvslength, byte* outputpvs )
Places the PVS for the given cluster in outputpvs. The return value is the number of bytes that were written; values in the rest of the buffer are undefined.
bool engine->CheckOriginInPVS( Vector origin, byte *checkpvs, int checkpvssize )
Determines whether the given location is within the given PVS.
bool engine->CheckB