The 々 symbol just repeats the kanji that comes before it. You'll see it from time to time, so take note of it, even though it doesn't really have any meaning of its own. So, essentially 中々 is the same as 中中. That being said, you have something that's middle x2. When something is even more middle than middle itself, it is very or considerably something or another.

The reading for this word is the kun'yomi reading, since it's like putting two single kanji together rather than a true jukugo word. To learn the kun'yomi reading, take a look at this mnemonic:

From the middle of the middle comes a sound. It is a knocking sound. Knock. Knock. Knock. You open up the walls around this thing. Then you open up the second set of walls (middle of the middle). Inside is an old man, who identifies himself as "the knocker." You go inside of him and find another knocker as well. That's why it's a knocker knocker (なかなか).