Serverless concept becomes quite desirable because the benefits seem pretty obvious, one is the cost savings and the other being elimination of managing servers! Billing is done with usage of the service on per second basis, and Aurora scales up or down the capacity depending on the load. AWS gives you the option of choosing the minimum and maximum number of Aurora Compute Units(ACU) between which Aurora will scale up or down depending on the number of incoming connections and CPU utilization.
Couple Aurora serverless with Lambda and you have a truly serverless application that is extremely cost effective and is capable of handling any incoming load on it's own. However you need to understand that there are quite a few drawbacks currently which might not make using Aurora serverless quite feasible for your production workloads. Like for instance
For enterprises, Aurora would work best for development purposes as you only need the instance to run during tests. They would also be suited for infrequently accessed internal systems that can tolerate latency in performance. Both cases will lead to cost savings that will be evident from day one. However, for adoption in production use, AWS would have to come with a way of tackling cold starts as they are quite significant. At the time of writing this, Aurora Serverless is available for 14 regions across the AWS realm, more regions soon to come. You can expect Aurora serverless for PostgreSQL in the near future too.
Test it out and let me know your thoughts in the comments below!