First of all, this is an IPv4 address; IPv4 address consists of 32 bits.
The /9 represents the number of bits for the network, meaning that they are reserved for the network, and you can't use them. So by a simple calculation,the number of bits for the hosts in this network is (32 - 9 = 23) and the number of hosts of this network is 2^23 - 2 Hosts ( we subtract 2 because one address is for the network address and the other is the broadcast address for the network)
Theoretically 192.168.0.1/8 is not allowed as a private network, since the network 192.168.x.x/16 is the private network, however if you want to use a private network with /8 you can use the 10.x.x.x/8.
What is meant by private network is a network that will not pass the gateway of the network. i.e. if you have for example a packet that has 192.168.1.10 (suppose that it is a host) as a destination, when it reaches the router or the gateway, it will be redirected to the local network, meaning it will not go through the gateway of the network and to the public network (internet).
But suppose you used 10.x.x.x/8 in your private network, then you have 2^24 - 2 hosts, and that is impossible to have in one network, thus you will have plenty and plenty of unused hosts, which brings us back to the reason of variable length subnet mask (VLSM) and classless Networks.
The reason behind the subnetting is because of the depletion of IPv4 addresses, because of huge network of hosts that was based on classfull networks as a class A network (refer to rch1231 post above).