The words "Rosh Hodesh" means the beginning of the month. Rosh Hodesh is considered a minor holiday and is celebrated with special torah reading and we also say the Hallel.

Hallel
The Hallel is a selection of mizmorim from Tehillim that are sung on the holidays as well as the beginning of every month (Rosh Hodesh) with the exception of Rosh Hashanah. There are times when the full Hallel is sung with a Beracha (blessing) and on certain holidays an abridged version is recited without a Beracha. One particular section, Odekha Ki, is sung out loud with the whole congregation in various tunes.

Hallel is recited on the following holidays:
    1.Succot- The full version is recited on all nine days
    2.Hannukah- The full version is recited on all eight days
    3.Pesach- The full version is recited only on the first two days
    4.Shavuot- The full version is recited on both days
    5.Rosh Hodesh-The partial version is recited on the beginning of every month.