Serverless computing is basically about getting servers in the cloud to execute some code snippets (FaaS) or utilise something like a database service with a pay-as-you-go pricing model (typically) and with no need to be concerned with capacity planning, horizontal scaling, hardware failure, etc.
‘Serverless’ is a bit of a misleading name because the code obviously still executes on actual servers, they’re just not maintained by you so can essentially be oblivious to their existence from a black-box perspective.
Note: for some reason I had always assumed serverless computing and microservice had something to do with each other. They don’t, but they’re occasionally used in the same project. Serverless is about how you run an app, while microservices are about how you architect an app. They’re both very frequently encountered in cloud computing.