a study.

adhyayanam means to study, to learn, to repeat/recite, etc. vEdham is studied under AchAryas by hearing from them and repeating the same. vEdha manthrams are also regularly recited as part of daily anushtAnams. anadhyayanam means to refrain from learning/reciting. There are certain times of the year when vEdham is not recited. This time is leveraged to learn other parts of sAsthram such as smrithi, ithihAsams, purANams, etc. Even through out the year, days such as amAvAsyai, paurNami, prathamai, etc., are not conducive for learning vEdham. As dhrAvida vEdham (4000 dhivya prabhandham) is also considered equivalent to samskritha vEdham, there is a tradition of not learning/reciting dhivya prabhandham during certain period of time. 
anadhyayana kAlam coincides with and encapsulates adhyayana uthsavam. adhyayana uthsavam is celebrated to glorify nammAzhwAr's ascending to paramapadham. The history of anadhyayana kAlam and adhyayana uthsavam are closely related in srIvaishNava tradition. The history is revealed elaborately in a grantham named "kaliyan aruL pAdu"