I have started galois theory recently, and curiosity quickly leads one to the subject of profinite groups. Although I have yet to be comfortable using these, I get what they are and we define them as we do, and when to expect them.
I stumbled on a paper which tries to prove that the absolute galois group of $\mathbb{K}(t)$ for K algebraically closed of characteristic 0, is the "free profinite group of rank |K|". So after this I tried looking up what a free profinite group is, which lead me to the subject of profinite completion.
Although it is pretty abstract, I am just about able to understand the definition (barely). My question to help me with this difficulty is:
What are some motivations for profinite completion? More specifically, why would one want to take a non profinite group and "turn it into" a profinite one?
Thanks in advance