Why do you need to have the ground of a power supply and the ground of a arduino hooked up together when working with a RGB LED strip and the 5v tied to the 5v on the power supply?
Because every electric circuit needs to have a complete return path.
You have to (be able to) look at the circuit and trace that path all the way around to the start.
The data pin from the Arduino needs to complete the circuit back to the Arduino ground.
Why.. the 5v tied to the 5v on the power supply?
You don't have to do that, but it is a convenient way to power the Arduino. You could power the Arduino from some other PSU or usb if you had a reason to do that. But if you do, don't connect the 5V on the Arduino to the 5V on the strip. You should never connect + of two separate power supplies together, even if they say they are the same voltage. They are never exactly the same, one will always be slightly higher than the other, and connecting them together could damage them.
In electronic, we DO NOT use the "potential", But we use "potential difference". In other words, we need to use a system of reference of potential. GND is a system of reference. When using two power source, We MUST connect GND of two power sources together. That is because, to make two system uses the same system of reference.
As @PaulRB said, you MUST NOT connect two VCC together.
It's not only for RGB strip but also for any two or more power sources. See more in https://forum.arduino.cc/index.php?topic=645712.0 (https://forum.arduino.cc/index.php?topic=645712.0)