At a really high level, SATA III had a 6Gbps data rate (8 bits per Byte, so 750MB/s) so most SATA SSDs were giving you 550MB/s at the most.

Conversely, NVMe is usually a PCIe x4 slot, which tops out at 4GB/s. Most M.2 NVMe drives will give you 3200MB/s, which is easily six times faster.

Edit: for a fun point of reference, old HDDs were about 60MB/s, with high latency on top of that due to seek time.