The Torah (also known as the Five Books of Moses or the Pentateuch) is divided into five books: Genesis, Exodus, Leviticus, Numbers and Deuteronomy. These books contain fifty-four sections or Torah portions, each called a sidrah.
Each sidrah (Torah portion) is divided into seven readings and the final few lines of the sidrah is called the maftir. The maftir is part of the seventh reading so it is effectively read twice. On certain special occasions the maftir is taken from another sidrah.
The haftarah is a passage from the Book of Prophets usually corresponding to the themes in the weekly sidrah. On festivals and for special Shabbatot different haftarot are read corresponding to the special event rather than to the weekly sidrah.
When a person is called to a Torah reading he/she says a blessing before and after that part of the sidrah is read. Different blessings are said before and after the haftarah is read.