Port forwarding is used to forward traffic coming in on your Meraki MX WAN IP on specific ports/port ranges.
1:1 NAT is to use an unused address (public IP) in the subnet of your MX's WAN interface as an alias for an address on the LAN side.
1:Many NAT is like a mix between the two. You can define multiple (unused) public WAN IP addresses to be used and configure port forwarding on each of them separately. Not all ports of a single public IP need to be forwarded to the same internal IP like with 1:1 NAT. And you're not limited to the Meraki MX WAN IP like with regular port forwarding.
A few examples:
Let's say your company owns the range: 7.7.7.0/24, your MX has 7.7.7.1.
Port forwarding would allow you to setup an HTTP server on the inside and forward traffic destined for 7.7.7.1:80 to 192.168.0.10:80.
1:1 NAT would allow you to forward all traffic (no matter what port) destined for 7.7.7.2 to 192.168.0.15.
1:Many NAT would allow you to forward port 80 on 7.7.7.3 to 192.168.17 and port 25 on 7.7.7.3 to 192.168.18.
There's also this article:
https://meraki.cisco.com/blog/2014/08/1many-nat-for-meraki-mx/
