The first 6 numbers of my IP address are always the same, but the last 4/5 or even 6 numbers not. What do these last 4/5 or 6 numbers specify ?

The last section(s) of the dotted quad identifies a single 'connexion' point. In the real world most ISP's don't have enough, so no single user, unless they pay for it has a single {so called static IP} connexion. So every time you log on you are given a new virtual location, though the root stays the same.

Oversimplified, but connexion now 123.456.789.123, next time 123.456.789.210. This still allows the root servers to identify who 123.456.789. belongs to e.g True Internet.

HTH

Regards

Edited May 7, 200818 yr by A_Traveller