This one’s pretty straightforward: just like a person is responsible for damage caused by his animals, he’s responsible for damage caused by fire. If a person lights a fire – even on his own property – he must pay for the damage it causes if he fails to contain it. (We’re not even speaking of a case of arson here. This is strictly in the case of unintentional damage. It’s a financial matter, not a criminal case.)
The Talmud discusses the details of this mitzvah, such as the reasonable distance a fire must be kept from a neighbor’s property, the case of one who sends fire by means of a reliable messenger, as opposed to one who sends fire by a child or by someone with limited mental capacity, damage caused by Chanukah lights, and more.
This mitzvah is incumbent upon the courts. In the Talmud, it is discussed in the second and sixth chapters of Baba Kama. (See pages 22a-23b in particular.) In the Shulchan Aruch, it is found in Choshen Mishpat 418. It is #241 of the 248 positive mitzvos in the Rambam’s Sefer HaMitzvos.