What are RNP and ANP in area navigation?
RNP is a numerical value that refers to the level of performance required for a specific published procedure.  If the procedure has an RNP 10, then the on-board navigation equipment must be able to calculate its position to within 10 nautical miles. If the procedure has an RNP 0.3, than the equipment must be able to calculate its position to .3nm.

ANP is the "actual" level of performance being experienced real-time. The on-board navigation equipment estimates the quality of the reception and determines how "reliable" it thinks its own position is.  If the estimate of reliability is high, then the ANP is lower.  An ANP value of 0.6 indicates that the navigation equipment is confident of its own actual position to within .6nm.  Essentially, this means that if the equipment puts a point on the map of where it thinks it is, there is a circle around that point with a .6nm radius and the aircraft is somewhere within that circle. 

If the RNP required value is lower than the ANP value, you cannot use that procedure.  If you're using a procedure, you must monitor the ANP value. If, at any time, the ANP goes above the RNP, you must exit the procedure. 

Here is an image of a Boeing 737 FMC displaying the current ANP (.06) and the RNP (2.0).  Courtesy of http://www.b737.org.uk