Lambdas are lightweight function calls that can be spawned on demand in sub-millisecond time and don't need a server that's constantly running. They can replace most server code in many settings, e.g. when building REST APIs that are backed by cloud services such as Amazon DynamoDB.
I've heard many impressive things about this way of designing your architecture, and it seems to be able to dramatically reduce cost in some cases, sometimes by more than 10 times.
The drawback is that currently there is a lot of vendor lock-in, as Amazon is (to my knowledge) the only cloud service that offers lambda functions with a really tight and well-working integration with their other services (this is important because on their own lambdas are not very useful).