There are many detailed mathematical descriptions of affine/taki transformations (check http://en.wikipedia.org/wiki/Affine_transformation for example). The simplest description is to say that it is a mathematical method of calculating the differences between the actual “sky” positions and the mount position. Basically it is used to tell the mount where it has to move in order to GOTO the required object. It uses the star catalog data from your planetarium program and the alignment data from the alignment process you completed at startup.
This documentation sometimes refers to the “encoders” in the mount. Strictly speaking, the mount doesn't have Optical Encoders, instead, the mount uses 32 bit ring counters to keep track of the stepper motor position. The more appropriate term to describe the stepper motor counters would be “RA position counter” or “DEC position counter”instead of “encoder” (or just “RA or DEC counter”).
The home position of the mount is the position where the telescope is pointing at the NCP (north celestial pole) or the SCP (south celestial pole). This is accomplished by setting the mount with the balance (counter-weight) bar point downwards and the scope point north or south.
Before powering down the mount, the mount should be returned to a park position. This position could be the same as the Home position. However, it is possible to define another position for the park position that might be preferable for special installations such as a permanent pier in a roll-off roof observatory. Parking the mount before shutdown means that the mount has a known place to start when power is returned and the mount is “unparked”. Recent versions of EQMOD allow several park positions to be defined so that mount could be (for instance) parked in a position suitable for maintenance.
POTH is part of the ASCOM software. Although you must use the ASCOM software itself, POTH is an add on feature to allow several programs to control the mount and other hardware at the same time using the same cable but POTH is no longer needed with EQASCOM.