( The CH is pronounced like CH in 'much', TH is pronounced like TH in 'with'. )
Chathur means four and Maasa means month. Chaathurmaasyam means 'pertaining to the four months'.
The four months in this usage refers from the eleventh day of Aashaadha ( fourth lunar month ) to eleventh day of Kaarthika ( eighth lunar month ). Usually, during this period that comproses the rainy (Varsha) and autumn (Sharath) seasons, the saints stay at a place ( normally they should not stay at the same place for more than three days) and observe some vows and perform some rituals. These rituals are collectively named Chaathurmaasyam.
It was once upon a time customary for saints and kings to perform special sacrifices during this period. Now, it is limitted to only Sanyaasis (monks), that too sparingly.
"After praying to Naaraayana, Nara, Sarasvathi and Vyaasa, then one should read the Jayam."
DEDICATED TO MY DEAR NIECE VYSHNAVI KRISHNA