Lambda is one of the coolest AWS services that allows to run code without provisioning or managing servers - so it is compute service. That is the developer can simply focus on the code and need not worry about the underlying infrastructure for running the code. Lambda is highly available and scalable and can execute 1000 times concurrently. Lambda currently supports NodeJS, Java, Python and C#.
Lambda can also integrate with other AWS services like S3, API Gateway, SNS and many more and allows to be triggerd by events on those services. For example, a Lambda function can be triggered by uploading, modifying or deleting a file in S3 or when data changes in DynamoDB and can be integrated with API Gateway to build a serverless infrastructure.
Lambda allows creating a fully serverless infrastructure, for example, a website can be written in angular js and therefore can be hosted in S3, call API configured using API Gateway which in turn calls Lambda which can retrieve data from DynamoDB. Thus a full web application can be created without creating a single server. Logs are also available from Cloudwatch making it easy to troubleshoot any issues.
Lambda is also very cheap and AWS gives many free execution (1 million free execution per month depending on memory configuration) before charging anything making it very cheap if not free to perform development and testing.