How does salt tank work?

I had an issue with compacted salt in the tank of my Silver Series equipment yesterday. I cleaned it all out and at the very bottom I found this black gunk that was mixed in with the slurry of partially dissolved pellets. I had to pull the float valve assembly out to clean it also.

My question is how does that whole float valve assembly work? There's only one water line running to the salt tank, I'm used to seeing one line that goes into a tank and a second line that goes out of a tank. I'm afraid that I may not have reassembled the whole thing properly and now the system won't work as designed.

I'm an industrial mechanic with 15 years experience so I can probably do this myself if I can get some guidance on how the system operates.