I.e. wrap your code as if it were a lambda function, and pass it to us. It will work when we call it just as well as when you do in the original environment.
Sounds like a better name would be "Amazon Macro", though. This is because the "lambda" (user's application) likely refers to features of the hosting environment and is influenced by them; it is not referentially transparent to place code on a server, even if the grunt work of setting up the surroundings is done by a "macro".
"Lambda" is a hot buzzword though, as some notable Blub languages have been scrambling to integrate them, whereas "macro" has a stained reputation.
1. The snippets of code you run in Lambda are called "cloud functions".
2. Lambda applications are generally event driven and stateless, which is a very functional idiom.
As other folks mentioned, however, you can use Lambda with non functional languages (like Java). So even though a Lambda application is inherently functional (small stateless functions communicating via events), you don't have to write in a functional style if you don't want to.