Wa `alaykum As-Salamu wa Rahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
Dear brother, it’s also our pleasure to say to you “`Eid Mubarak!”
May Allah shower us with His blessings and bounties!
As regards your question, we’d like to cite for you the following:
Islam teaches Muslims how to celebrate the `eids. On these days, the Muslims take a bath and wear their best clothes. Even though fasting is not permitted on the `eid days, yet, the major part of the celebration is not eating or drinking; rather, it is a prayer that brings Muslims together to remember Allah's bounties and celebrate His glory and greatness.
The `eids and their celebration in Islam carry a distinctive meaning and spirit. They are totally different from the celebrations in other nations and cultures. For other nations, a holiday is a chance to immerse in worldly pleasures, or to involve oneself in prohibited acts to the utmost. Not so for Muslims! For Muslims, the `eid is an occasion to increase in good deeds. Each `eid marks the conclusion of an important worship, and the determination to continue in obedience and submission to Allah (Glorified be He).
In moments of extreme pleasure or sadness, a Muslim never forgets his Lord's greatness, might, glory, and watchfulness (Glorified be He). A Muslim's actions are always controlled by this continued remembrance and awareness.
Thus the `eid is not an occasion to take a vacation from Islamic responsibilities and commitments, nor to waste time and money in extravagance. It is not "fun for the sake of fun". Rather, it is controlled and directed rejoicing that is of ultimate and definite benefit for the Muslim.
The `eid is a chance to multiply good deeds by bringing happiness and pleasure to the hearts of other Muslims, by helping and supporting the poor and needy, and by getting involved in pastimes that emphasize the strong and serious Islamic character.
Excerpted with slight modifications from: www.islaam.com