Lineage
History
noun
The main reason behind your connection to some people is your lineage or history. Lineage and history tie people (especially families) together.
This word can be used for people with a prestigious family lineage as well as for historic buildings, especially temples and shrines.
You didn't learn this reading for 由 with the kanji, so here's a mnemonic to help you:
If you had good lineage you'd never make a U-ey (ゆい) on the highway. That's dangerous, and people with good lineage and a long history would simply never do such a thing.
京都の清水寺は由緒あるお寺だ。
Kiyomizu Temple in Kyoto is a temple with a long history.
由緒ある家の人でも、いい人だとは限らない。
Just because he has a prestigious lineage, it doesn't make him a nice person.
日本で最も古い由緒ある神社です。
It's the oldest and most venerable shrine in Japan.