Eid Mubarak is a traditional Muslim greeting reserved for use on the festivals of Eid ul-Adha and Eid ul-Fitr. The phrase translates into English as "blessed festival", and can be paraphrased as "may you enjoy a blessed festival" (Eid refers to the occasion itself, and Mubarak means "Blessed")
Muslims wish each other Eid Mubarak after performing the Eid prayer. The celebration continues until the end of the day for Eid ul-Fitr (or al-Fitr) and continues a further three days for Eid ul-Adha (or Al-Adha). However, in the social sense people usually celebrate Eid ul-Fitr at the same time as Eid ul-Adha, visiting family and exchanging greetings such as "Eid Mubarak". This exchange of greetings is a cultural tradition and not part of any religious obligation.

Source: wiki