Eid means "Celebration" and refers to the occasion itself, and Mubarak means "blessed"; for example: "Eid Mubarak, sister!"
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 after Ramadan and Eid-ul-Adha in the month of Dhul Haj (12th and Final Islamic month), visiting family and exchanging greetings such as "Eid Mubarak"
This exchange of greetings is a cultural tradition and not part of any religious obligation