Eidgah or Idgah is an open-air mosque

Mosque

A mosque is a place of worship for followers of Islam. The word is likely to have entered the English language through French , from Portuguese , from Spanish , and from Berber , ultimately originating in — . The Arabic word masjid literally means a place of prostration...

 usually outside the city (or at the outskirts) to perform Eid ul-Fitr

Eid ul-Fitr

Eid ul-Fitr, Eid al-Fitr, Id-ul-Fitr, or Id al-Fitr , often abbreviated to Eid, is a Muslim holiday that marks the end of Ramadan, the Islamic holy month of fasting . Eid is an Arabic word meaning "festivity," while Fiṭr means "breaking the fast"...

 and Eid al-Adha salah.

It was a practice of Prophet Muhammad

Muhammad

Muhammad |ligature]] at U+FDF4 ;Arabic pronunciation varies regionally; the first vowel ranges from ~~; the second and the last vowel: ~~~. There are dialects which have no stress. In Egypt, it is pronounced not in religious contexts...

 to perform Eid Salaah in Eidgah at the outskirts of the city. Hence, It is Sunnah to perform Eid Salaah at the Eidgah.

The very first Eidgah was at the outskirts of Medina

Medina

Medina , or ; also transliterated as Madinah, or madinat al-nabi "the city of the prophet") is a city in the Hejaz region of western Saudi Arabia, and serves as the capital of the Al Madinah Province. It is the second holiest city in Islam, and the burial place of the Islamic Prophet Muhammad, and...

 nearly 1000 footsteps from Masjid al Nabawi

Al-Masjid al-Nabawi

Al-Masjid al-Nabawi , often called the Prophet's Mosque, is a mosque situated in the city of Medina. As the final resting place of the Islamic prophet Muhammad, it is considered the second holiest site in Islam by Muslims and is one of the largest mosques in the world...

.^,

Eidgah in Sharia

• Complying to the Sunnah, performing of the Eid Salaah on the outskirts of the town is better and more virtuous, than performing it in the town.
• The Eid Salaah performed in the Masjid is complete, but performing it in the Eidgah is Sunnah. Without any valid excuse, not to read the Eid Sunnah in the Eidgah is contrary to the Sunnah.
• The Eid Salaah should be a huge gathering on the outskirts of the town. In this way the might and power of Islam is manifested. In the big cities it is difficult to make Eidgah on the outskirts of the city, therefore a huge open plain should be chosen for the Eidgah or according to the need, it can be performed in the Masjid, which will be correct. But as far as possible, one huge gathering is more superior compared to many small Eidgahs.
• Performing of the Eid Salaah in the Eidgah is Sunnat-e-Muak'kadah. Without any valid excuse, the one who does not perform his Eid Salaah in the Eidgah is worthy of being reprimanded and taken to task and this kind of a person is a sinner. If the Eidgah is a distance away and it is inconvenient for the old and sickly, then the Jurists have given permission for them to perform Eid Salaah in the Masjid.