please define terms

[Larry Honig]

I'm sorry to brutally expse my ignorance of terms, but I may not be the
only neophyte here so I will do it anyway. What exactly is meant by /24,
/19, /xx??  It seems that the "buying power" represented must be greater
as the denominator decreases. Would a /1 allocate all 4 billion IPs?
How does this map into - lets say - a scheme where I as an ISP would
like to allocate (in IPv4 syntax) all the numbers between (for example -
not a real sequence) 99.128.51.0 and 99.128.51.255? Also, under IPv6 how
would this look? Please give a specific example if possible. Thanks in
advance.