Serverless in that context essentially means “somebody else's server(farm)”. It frees you from some of the infrastructure/admin involved in server sizing & upgrades, backups, availability management, and so on.
It can be very attractive to teams who don't want to have an internal expert for all that, or to buy huge hardware to deal with spikes in activity that only happen occasionally⁰. Just being able to spin up a large DB for some tests without worrying about available space, how much it will compete for this like CPU/IO with your other DBs¹, etc, can be very convenient.
It can work out quite expensive in terms of price/performance ratio, if those factors are not a benefit to you.
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[0] or happen regularly but usually for only a short time
[1] usually these things are capped, or have a burstable cap, so “noisy neighbours”² are not the huge problem they can often be on cheap shared hosting
[2] unless you have explicitly pooled resources (like Elastic Pools for Azure SQL) without per-object limits, in which case your own activity could be harmful noise
