The Rawdah is the area between Hz. Peygamber's grave (or originally his house) and his pulpit (minbar) in Masjid al-Nabawi. Hz. Peygamber (sallallahu aleyhi ve sellem) described it as 'a garden from the gardens of Paradise,' indicating its immense spiritual significance. Prayer in this area is one of the most virtuous acts a visitor to Medine can perform, as it combines the virtue of praying in Hz. Peygamber's Mosque (which equals 1,000 namazs elsewhere) with the specific blessing of this sacred space.
Sheikh Ibn Baz stated that the haci should try to pray two rak'ahs in the Rawdah if possible, make heartfelt dua, and then send salam upon Hz. Peygamber from whatever location they are in the cami. He emphasized that the virtue of the Rawdah does not mean that namazs in other parts of Hz. Peygamber's Mosque are without reward — the entire cami carries immense virtue. A person who cannot access the Rawdah due to crowds should pray anywhere in the cami and still earns the multiplied reward.
Sheikh Ibn Uthaymeen warned against several improper behaviors that occur at the Rawdah: pushing and shoving others to reach the area (which is sinful and negates the reward), extending namaz or dua for an unreasonable time while others wait, touching or wiping the pillars or walls seeking blessings (this has no basis in the Sunnah), and treating the Rawdah visit as more important than the farz namazs (some visitors miss the congregational namaz to sit in the Rawdah, which is misguided).