Possession is a book written by A. Byatt.

In my opinion she decided to entitle her book in this way because of two reasons.
The first one: she wanted to underline the deep relationships between the characters in the story.

In telling this it is very important to focus the attention on the differences between three words which appear similar: possession, ownership and property. While I was reading the three definitions I immediately had the impression that the word possession had a deeper meaning. While the words ownership and property refer to "the act of having and controlling something" or to "the state or fact of being an owner", under the word possession I find also other definitions: "a mania restricting to one thing or idea", "being controlled by passion or the supernatural" and "obsession by a feeling, idea". Therefore in the book the word possession may refer to the relationships between the characters (for exapmle one character wants to posses his/her beloved) and in particular to the couples Ash-La Motte (with the presence of Ellen and Blanche) and Maud-Roland (with the presence of Val and Fergus).  
The second thing is that the word possession may be connected with the strong will of the characters to find and to keep jealously some important manuscripts/letters.