The narrative of Clotel plays with history by relating the "perilous antebellum adventures" of a young mixed-race slave Currer and her two light-skinned daughters fathered by Thomas Jefferson. Because the mother is a slave, according to partus sequitur ventrem, which Virginia adopted into law in 1662, her daughters are born into slavery. The book includes "several sub-plots" related to other slaves, religion and anti-slavery. Currer, described as "a bright mulatto" (meaning light-skinned) gives birth to two "near white" daughters: Clotel and Althesa.
After the death of Jefferson, Currer and her daughters are sold as slaves. Horatio Green, a white man, purchases Clotel and takes her as a common-law wife. They cannot legally marry under state laws against miscegenation.
Her mother Currer and sister Althesa remain "in a slave gang." Currer is eventually purchased by Mr. Peck, a preacher. She is enslaved until she dies from yellow fever, shortly before Peck's daughter was preparing to emancipate her.
Althesa marries her white master, Henry Morton, a Northerner, by passing as a white woman. They have daughters Jane and Ellen, who are educated. Although supporting abolition, Morton fails to manumit Althesa and their daughters. After Althesa and Morton both die, their daughters are enslaved. Ellen commits suicide to escape sexual enslavement, and Jane dies in slavery from heartbreak.
Green and Clotel have a daughter Mary, also mixed race of course, and majority white. When Green becomes ambitious and involved in local politics, he abandons his relationship with Clotel and Mary. He marries "a white woman who forces him to sell Clotel and enslave his child."
Clotel is sold to a planter in Vicksburg, Mississippi. There she meets William, another slave, and they plan a bold escape. Dressing as a white man, Clotel is accompanied by William acting as her slave; they travel and gain freedom by reaching the free state of Ohio. (This is based on the tactics of the 1849 escape by Ellen Craft and William Craft). William continues his flight to Canada (an estimated 30,000 fugitive slaves reached there by 1852). Clotel returns to Virginia to try to free her daughter Mary. After being captured in Richmond, Clotel is taken to Washington, DC for sale at its slave market. She escapes and is pursued through the city by slave catchers. Surrounded by them on the Long Bridge, she commits suicide by jumping to her death in the Potomac River.
Thus died Clotel, the daughter of Thomas Jefferson, a president of the United States.
窶披�窶年arrator of Clotel, Page 182
Mary is forced to work as a domestic slave for her father Horatio Green and his white wife. She arranges to trade places in prison with her lover, the slave George. He escapes to Canada. Sold to a slave trader, Mary is purchased by a French man who takes her to Europe. Ten years later, after the Frenchman's death, George and Mary reunite by chance in Dunkirk, France. The novel ends with their marriage.

Question: Why can't Clotel and Horatio Green marry?
Answer: They cannot marry because there are state laws that forbid inter-racial marriage. 
Alternative answer: They were different races and is was illegal