“This color really goes well with your skin tone.”
You're a makeup artist. You're choosing a lipstick to put on a customer. You think this a good color of lipstick for her, so you say this.
This color really goes well with your skin tone.
This phrase means that two things look good together. It's a similar idea to "matching". You could also say in this situation:
This color really matches your skin tone.
But the word "match" can also mean that two things look the same as each other. If your shirt and shoes "match", it might mean that they're the same color. But if you say that they "go well" with each other, it just means that they look good together:
Those shoes go well with that shirt.
Another variation of "go well" — "go well in ___" — can be used to talk about decorating a room:
Your "skin tone" is the specific color of your skin. This phrase is often used when talking about makeup or clothes. People try to match their makeup and clothes to their skin tone and hair color.
The word "tone" is interesting because it can be used for:
a range of colors:
I mostly wear neutral colors and earth tones.
"Earth tones" are colors like brown, dark orange, and dark red.
At the tone, please leave your name and a detailed message.
(This is the automatic message that you hear on people's voice mail when they don't answer their phone.)
I can tell by the tone of your voice that you're angry.
the social atmosphere:
The tone of their meeting was extremely tense.
The tone of the conversation suddenly shifted.