There is no clear definition with universal agreement. It's a hype-y term applied with... varying levels of rigor.

However, roughly speaking, "serverless" rolls together 3 features:

1. Fine grained pay-per-use (e.g. pay for a query by the number of rows scanned)

2. The pricing dial goes down to zero when usage is small enough.

3. You generally don't control VM/instance-level scaling but something closer to the abstraction level of the product being claimed as "serverless". For example in planetscale you get no control over how many mysql instances actually run your queries. This is great for reducing operational complexity but not so great for controlling performance. Performance tends to be quite opaque -- for example there's nothing I can find in Planetscale's docs about latency and throughput. The operational benefits are real, though. It's a tradeoff.