Not having to provision and maintain servers and the software running on it is by far the greatest advantage of running a serverless architecture. Not only this can help reducing operational costs but it also frees up software engineering time that could be spent in more valuable tasks.
Another advantage is the scalability of a serverless environment once it is well architected in independent components. In fact, a serverless architecture is stateless and event-driven and can be easily scaled up and down by adjusting the resources and parameters of the single components. For example, memory allocation is a parameter in the lambda function; running out of storage space is not an issue since S3 provides virtually infinite storage space.
Finally, the serverless architecture is highly available since it relies on AWS managed services like API Gateway, Lambda, and S3: the architecture will go down only if and when AWS experiences an outage.