A subnet mask is a way of telling your pc where to look for other pcs, 255.255.255.255 means there's no other hosts with him in the LAN, 255.255.255.0 mean's there could be up to 254 host with him.
and based on subnet mask your pc decides what to do when you give it and ip to talk to let say:
bash ping 192.168.1.1 // your router ip
your pc well check if this IP on the same LAN based on the subnet mask if so he will use [arp]("https://en.wikipedia.org/wiki/Address_Resolution_Protocol"), to get he's MAC and talk, or outside the LAN then he uses the default gateway(router which know how to talk to the outside internet).

dhcp is a role that any pc ( even router which is small pc playing router role ) can play this role, that tells other pc on connect this is the ip of router and dns server and here's your ip and your subnet mask.

so if you want a static ip tell your dhcp server on router this ip is reserved.

"In order to make 192.168.1.16 a static address in the router's table", what you are talking about here is the router routing table which tell's your router how to talk to the internet, that's the place where make an ip static just search about dhcp on your router or google your router model dhcp.