What is the imperative mood and how do you form it?

The imperative mood in French is used to give commands and make suggestions, and translates into English as the commanding "do this!" or the suggestive "let's...". 
The commanding imperative comes from the "tu" or "vous" form of the verb depending on the formality and plurality (tu is singular and informal, vous is formal singular or plural) required for the person you are commanding. Forming this mood is simple. Take the form of the verb and remove the pronoun "tu" or "vous", such as "mangez!" meaning "eat!" (singular formal/plural). One rule to remember is that for regular -er verbs and "aller", the final -s of the tu form is omitted ("mange!") and is sometimes added back on when followed by a vowel sound (such as "va" but "vas-y"). There are also irregular verbs in the imperative including avoir and être.  
The suggestive "let's..." comes from using the "nous" form of the verb without the pronoun "nous", such as "mangeons ensemble" meaning "let's eat together". Again some verbs like avoir and être are irregular.