MARHABAN YA RAMADHAN
Taraweeh is derived from the Arabic root word, raaha, which means to rest, relax and use as recreation. It is so called because the believers used to prolong it. After every four raka'ats they would stop for rest and relaxation and resume until taraweeh was complete.
'Aishah (raa) has been reported as saying:
"The Messenger of Allah (saas) observed Taraweeh prayer in the Masjid one night and people prayed with him. He repeated the following night and the number of participants grew. The companions congregated the third and fourth night, but the Messenger did not show up. In the morning he told them, "I saw what you did last night, but nothing prevented me from joining you except my fear that it might be made mandatory on you in Ramadan."
(Bukhari and Muslim)
No one should neglect Taraweeh without a good reason, for it is part of physical and spiritual training, for its observation soon after Iftar insures timely and proper digestion of food. Besides, there are spiritual rewards awaiting the observers of this prayer. No one would like to leave the Masjid before the prayer is over.
Everybody should attend the Masjid prayers, including women, provided they are properly covered.
The Messenger of Allah said: "Prevent not the women servants of Allah, from going to the Masjid of Allah."
However, when they attend the Masjid they should wear no perfume, nor raise their voices, and or show their beauty.
Allah (SWT) states: "...they should not display their beauty and ornaments except what (must ordinarily) appear thereof..." (Al-Qur'an, 24:31)
[excerpt from : TARAWEEH (link here)]