I got married on February third.
In February, air tickets to Japan are very cheap.
Our affair began in February of last year.
The kanji 月 means both month and moon (because moon cycles take about a month, presumably). So, what is the number two month? It's not January... it's not March... it's February!
This is a jukugo word, which usually means on'yomi readings from the kanji. That is true with this word as well. Make sure to take note that 月 is using the がつ reading and not the げつ one. This is true for all "month words" in Japanese.