Hi Dore
''Eid'' means feast or festival in Arabic and ''Mubarak'' means blessed, so Eid Mubarak means a blessed or happy feast.
Yes there is a connection between Haj and Eid, as Eid is celebrated on the 10th day of month of Hajj after the annual pilgrimage to Makkah in Saudi Arabia.
Eid ul-Adha is celebrated as a commemoration of Prophet Ibrahim's willingness to sacrifice his son for Allah. On this day Muslims sacrifice animals which have been deemed Halaal, or fit for sacrifice. They not only eat the meat themselves but distribute it amongst their neighbours, relatives and the poor and hungry.
manal