It means "look at what I'm doing or have accomplished so far" If I was building a house with playing cards, and it was very tall and impressive - I would say to you "look what I've got going here" - "what I've got going" is the house made of the cards, and I'm still stacking cards to make it taller so I would use the term "got going" because it is still in progress. If I was FINISHED, I would instead say "look what I've DONE here" since its completed.

I don't remember the episode it it basically means "Hey look at me!"