Under U.S. law, a license is a contract. In fact, an EULA is an "end user license agreement."
The difference between a license like the AGPL and a normal contract is in how the contract is formed. Normally a contract requires explicit acceptance to be valid, but for licenses implicit acceptance is allowed, such as by using the licensed material after having been showed the license governing the use of that material.
Excerpt for where to start reading: "This right to exclude implies an equally large power to license—that is, to grant permission to do what would otherwise be forbidden. Licenses are not contracts: the work's user is obliged to remain within the bounds of the license not because she voluntarily promised, but because she doesn't have any right to act at all except as the license permits."
Under U.S. law, a license is a contract. In fact, an EULA is an "end user license agreement."
The difference between a license like the AGPL and a normal contract is in how the contract is formed. Normally a contract requires explicit acceptance to be valid, but for licenses implicit acceptance is allowed, such as by using the licensed material after having been showed the license governing the use of that material.