I've read that it's somehow connected with the Canon Law, but I'm not sure. I'm really interested in finding the answer.
Here's the OED etymology:
A phrase appended to names of relationship, as father, mother, brother, sister, son, etc., to indicate that the relationship is not by nature, but in the eye of the Canon Law, with reference to the degrees of affinity within which marriage is prohibited. These forms can be traced back to the 14th century. Formerly -in-law was also used to designate those relationships which are now expressed by step-, e.g. son-in-law = step-son, father-in-law = step-father; this, though still locally or vulgarly current, is now generally considered a misuse.
source: “-in-law.” The Oxford English Dictionary. 2nd ed. 1989. OED Online. Oxford University Press. 15 June 2011 <dictionary.oed.com>
Essentially, you cannot marry anyone related to you "in-law" because Canon Law treats them identically to an actual brother, sister, etc.
The usage of "in-laws" came a long way, from Anglo-Norman:
in-law XIX. sb. use of phr. denoting connection by marriage, e.g. brother-in-law (XIII), father-in-law (XIV); after AN. en ley, OF. en loi (de mariage) ‘in law (of marriage)
It is just to denote that this "brother" is only a brother due to marriage, and is therefore a brother by law, not by birth.