Grishma is short for Grishmarutu, the Sankrit word meaning summer (as in the season). This is one of the six seasons,each lasting two months. (viz. Vasant, Grishma, Varsha, Sharad, Hemant and Shishir.)

It falls in the two months of Vaishakh and Jayeshtha as per Hindu calender or April - May as per Gregorian calender.
It is preceded by Vasant ( Spring season and follwed by Varsha ( Rainy season)