IP addresses are numbers, each 32 bits long.

A subnet of a given prefix length is a set of addresses for which the first prefix length bits are the same.

So 10.0.0.0/16 means all addresses where the first 16 bits are 00001010 (10) 00000000 (0).

If you wanted a set of addresses with the first 24 bits the same as 10.0.0.64, that would give you all addresses between 10.0.0.0 and 10.0.0.255 (inclusive), which we conventionally call 10.0.0.0/24.

But you already gave 64 of those addresses to someone, so you need to find 256 addreses all with the same first 24 bits and that is 10.0.1.0/24.