The main benefit of NVMe is speed, where NVMe is fundamentally different than SSD is in that it is an end to end standard for both connectivity and flash based storage. Meaning you don't only get the speed benefits of flash storage, but you also get a modern connection between the flash storage and your PCIe bus.
What the heck does that mean?!?
SSDs use SATA or SAS connectivity to connect the drive to the motherboard. NVMe however includes connectivity. So where you can pull out an old hard drive and replace it with an SSD, because they are both SATA/SAS interfaces, you can't do this with NVMe.
NVMe utilizes m.2 and u.2 connections, there is no SATA/SAS connectivity, which means you aren't slowed down by old technology.
Basically NVMe removes the bottlenecks in current SSD drives, to get up to 5x performance.