Summary:
Fitr means opening and since in this day (Shawwal 1) Muslims break one month of fasting is called Eid al-Fitr. Eid al-Fitr is the first day of Shawwal; thus, by seeing the new moon of the month of Shawwal on the 29th of Ramadan or after 30 days of Ramadan, Eid al-Fitr is confirmed.
Fitr means opening and since in this day (Shawwal 1) Muslims break one month of fasting is called Eid al-Fitr. Eid al-Fitr is the first day of Shawwal; thus, by seeing the new moon of the month of Shawwal, on the 29th of Ramadan or after 30 days of Ramadan, Eid al-Fitr is confirmed. According to some hadiths, the month of Ramadan is always 30 days and will never be less. Some of scholars of the past supported these hadiths. However, some hadiths say that the month of Ramadan like other months can be 29 or 30 days. Most faqihs support these hadiths.
Muslims are not only celebrating the end of fasting, but thanking Allah for the help and strength that he gave them throughout the previous month to help them practice self-control. The festival begins when the first sight of the new moon is seen in the sky. Muslims in most countries rely on news of an official sighting, rather than looking at the sky themselves. The celebratory atmosphere is increased by everyone wearing best or new clothes, and decorating their homes. There are special services out of doors and in Mosques, processions through the streets, and of course, a special celebratory meal—eaten during daytime, the first daytime meal Muslims will have had in a month. Eid is also a time of forgiveness, and making amends. The Islamic Eids are unique in every way. To them there can be nothing similar in any other religion or any other socio-political system. Besides their highly spiritual and moral characteristics, they have matchless qualities: Each Eid is a wholesome celebration of a remarkable achievement of the individual Muslim in the service of Allah.
Source: http://english.tebyan.net/newindex.aspx?pid=27394&Keyword=+Eid+al-Fitr