We have discussed the relevance of usual/daily prayers (read namaz) in the condition of Fasting already. In addition to it there are a special set of namaz especially prayed in this month named as Taraweh.
Taraweh is a exclusive set of Salat popularly believed to be prayed in a set of 20 prostrations daily but few sects believe it to be of 12 sets, and few others even propagate it to be a set of 8. It becomes applicable with the sighting of the crescent of Ramadhan from the eve of the first day itself and continues till the crescent of Eid(festival) is sighted.
As it is obligatory in Taraweh to halt for atleast a minute after a set of every four prostrations, it is named so after the arabic word 'raha' which means 'to halt'. There is also a special prayer (dua) to be recited in these breaks to ensure we rest atleast minimally, and do not engage in distraction during the breaks.
This tells us of the importance of rest and how to balance between work and rest in life too.
Taraweh is not obligatory but highly recommended and also seen from the example set by our prophet Mohammed (peace be upon him), and performed after the usual obligatory namaz of after-nightfall.
For men it merges with the other form of prayer- reciting the whole of Quran in this month. As their pray in congregation and verses of Quran is an important part of every namaz, the cleric leading the group recites the verses of Quran from beginning to end during Taraweh throughout the month, usually completing on the eve of 27th Fasting(probable Shab e Qadr).
As women are given the provision of performing Namaz in the comforts of their homes, we can perform the Taraweh with any or even one small chapter from the Quran whichever we can recall from our memory. We try and complete a full recital of the Quran as and when we find time to do so.
The Holy book has special relevance to this month as it was sent down on this earth from heaven, in its entirety and as a guidance to humankind, in this month and on the night of Shab e Qadr.
It is even said in the Hadiths (events that occured during our prophet's lifetime, and info generated via him) that The Holy book and our Fastings will plead on our behalf for Divine forgiveness on the Day of Judgement.
As for the other form of prayer I mentioned, Dua- asking directly for Allah's mercy and fulfillment of our wishes, we can do so anytime of the day or year, but the speciality of this month is that Allah has promised to fulfill our every wish asked in the state of Fasting, and the moments of Sehar and Iftar are such which are highly praised to be those in which our prayers are never rejected, provided they are asked in the right spirit of humanity and sans every vice and unfair intentions.
And as we human's wisdom is limited to our knowledge and our wishes may also be influenced by our desires which may not always be better in our stride, Allah has even clarified either of the three ways in which He accepts our prayers;
~ He might grant us exactly what we asked for, immediately or when the time is right,
~ He might protect us from any impending danger or loss instead, or
~ He might chose to redeem our wishes on the Day of Judgement as rewards.