insertion into a set takes O(log n) time, which means ?

I have heard about big O notation which desribes how memory usage changes when input changes.

But log n ? n is probably the number for input values but i don't get it

let's say i have 25 inputs and log 25 with base what is that ? probably base 10, but could some one please please give me simple example and explain how this thing works?

thanks