The Twins, also known as the Crossing, is the name of the fortified river crossing on House Frey's territory in the Riverlands. The bridge that one must use in order to cross the Twins has benefitted House Frey because they charge hefty fees for anyone to cross it. It is the seat of House Frey.
It took the Freys three generations to complete the Twins, around six hundred years ago. The Twins quickly became one of the most strategically important castles in Westeros, as anyone who wanted to get in or out of the North had to pass through the castle. The Freys grew very rich from this, since any crossers had to pay for passage.
The Red Wedding
A wedding between Lord Edmure Tully and Roslin Frey was held at the Twins. This wedding was a trap for the Tullys and the Starks, however. The wedding quickly turned into a massacre known as the Red Wedding, which resulted in the Starks and the Tullys being deposed as great houses. The Freys expected to become the Lords Paramount of the Trident after this, but that title went to House Baelish instead.