Some DHCP servers can serve up multiple scopes (scope ~subnet range and parameters specific to that segment).
In order to use (for example) four subnet blocks you need for interfaces on which to apply them.
For example, if you had a Cisco router with four ethernet interfaces, you could use one of the subnet blocks on each of the Ethernet interfaces. IN teh case of CIsco routers, you can add additionaol blocks of addresses to an interface with a "SECONDARY" keyword (for example, you could have a 10.1.1.0/24 address as the primary block, and a 172.16.0.0/16 address as a "SECONDARY" block.
This is usually used when you are migrating from one address scheme to another, so all of the clients can still function, even though some are on one address block that the rest are on another. In any other practical context, it's a silly thing because it doesn't really accomplish anything.
Otherwise, the subnetting example you've posted would allow you to break one large address block into several, which would usually be used to permit several locations to use a portion of the original block / address space ... or several LAN segments .... but each segment needs its own interface on the router.
If you have a standard SOHO router with a WAN interface (to a BB or DSL modem) and an Ethernet interface (usually ~four or eight switch ports on the same routed interface), then subnetting would do you no good .... you only have one interface for which you can select the address space.
You can subnet and reduce the potential count of hosts on the network; the .240 mask gives you addresses for fourteen hosts ... that would be all you can use ... if you used an address outside of that block, it would be an invalid address and the client couldn't communicate.
What are you trying to do, and what equipment are you trying to do it with?
FWIW
Scott