Adhyaaya means a chapter.
The literal meaning of the word is "reading" or "study", indicating the quantum of text the reader is supposed to be able to read in one go with ease.
Most of the works, poetry or prose, are divided into parts of different names. Prominently, some shloka's are grouped together and called adhyaaya.
In Mahaabhaaratham , the main book is divided into parva's which are sub-divided into sub-parvas. Each sub-parva is divided into some adhyaaya's containg some
shloka's , the number of such shloka's being the choice of the composer. Usually, this number varriedly ranges from as small as 10 to as big as 100.
The number of adhyaaya's in Mahaabhaaratham is considered differently by different scholars and different recensions. The chapter 51 of Aaadi pava mentions that the Mahaabhaaratham consists of 2000 Adhyaayas, 100 parvas and 100000 Shlokas (stanzas). Some opine that these round figures about Adhyaayas, Shlokas and Parvas were meant to be understood as meaning 'nearly those many.' As can be seen from the preface of 1935 PPS Sashtry Edition, the number of Adhyaayas varies from 1944 to 2312 in various editions.
Also, note that the count of Adhyaayas starts at the beginning of the main parva only, but not from the beginning of each sub-parva. That is to say, for examlple, if a sub-purva ends with chapter 37, the next sub-parva runs from chapter 38.