Sirens were sea-nmphs who lured seamen into death with their enchanting singing. Every mortal who heard their song can't think of anything else until a crash on the rocks at siren's island became inevitable.
Sirens were daughters of the river god Achelous and companions to Persephone. When she was abducted by Hades, Demeter, Persephone's daugheter gave them wings to help them at the search for Persephone. When sirens gave up of search, they were cursed to keep partly human and partly bird body.
Some sources claim they were actually cursed before - at abduction, but it's hard to say which one is is more believable. In all versions they were confined at the island, where they temted sailors until one of them escaped their charms. It was Odyssey, who ordered his crew to plug their ears with wax and tie him at the mast. When he successfully heard their song and survived they reportedly commited suicides.
While Greek writers stayed faithful to their human-bird combination, Romans and especially later artists started to confuse sirens with mermaids (half fish instead of half birds). You can check the page about John William Waterhouse's paintings of mermaids who loved to portray both. Here are some paintings of sirens:
The general idea behind the painting above is a presentation of the sea-fairy or te siren as the temptress who's song is fused with the songs of the sea birds and is fatal for the sailors who stray from the safety because of their charm.
Rossetti (1828-1882) is well-known by the usage of symbols and his fondness for women with red hear. Here you can find more about him, his models and famous paintings of redheads in general.