Hello! I'd say it means "now you're all set up, go and try it/you do it by yourself/you can go and do it/it's your turn" Eg: - a toddler wants to jump into the swimming pool: you equip him/her with floaters, then send him/her to the water "there you go!" - it's your turn to walk onto the stage in some play; a friend gives you a slight push on the shoulder and says "there you g
Also, when complying with someone's wishes to bring something.
The waitress in a restaurant brings the food and says, "There you go", meaning "Here is your order", "Here's what you wanted".
If someone asks me for a stapler or pad of paper or something like that around the office, I can hand it to them and say, "There you go", meaning "Here's what you wanted".
It seems nowadays people are speaking 'There you go' in senses similar to 'There you are'/'Here you are'. However, according to OED, 'There you go' was originally used when a speaker wants to call the hearer's attention to their repeated behavior (talk, action, etc) to express the speaker's disapproval of it. All of the five uses quoted in OED are as follows; 1) The