"相性が良い" is a phrase that means "to go well together". It is used when some people/things seem to be a good match. "気が合う" is a synonym and it is used when some people get along well with each other. "相性が悪い" is the opposite expression.
Ken and Leo are drinking after their work.
- Ken: Cheers! Beer and sausages are a perfect match!
乾杯！ビールとソーセージは合う(or相性が良い)ね！ - Leo: Yeah. By the way, how's your project going?
うん。ところで、プロジェクトはどう？ - Ken: A new manager joined last week. He is a little arrogant so I think that I don't get along with him.
先週新しいマネージャーが入った。ちょっと偉そうで、僕と気が合わない(or相性が悪い)気がする。
Meg is browsing horoscopes with her boyfriend.
- Meg: What's your zodiac sign?
星座は何？ - Tom: I'm a Cancer. I don't really believe in horoscopes.
蟹座。星占いなんて信じないよ。 - Meg: Let me see...it says that you are compatible with a Pisces. Oh, that's me! You still don't believe in horoscopes?
えっと...魚座と相性が良いって。あっ、私じゃん！まだ、信じない？ - Tom: Wow, I believe it. I think we are definitely made for each other.
おー、信じるよ。俺等、本当に相性が良い(or気が合う)んだ。
Meg and her boyfriend are shopping at a clothes shop.
- Tom: How long is it going to take? What do you want?
あとどれくらいかかる？何が欲しいの？ - Meg: I'm looking for a scarf that goes with today's dress. Oh, I like this one. What do you think of it?
今日の服に合うスカーフを探しているの。あっ、これいいな。どう？ - Tom: I like it. I think that scarf and the color of your dress go well together.
いいね。そのスカーフは洋服の色と合う(or相性が良い)と思う。