I'm going to be honest and say now that this might be the worst picture I've seen taken in the last 5 years, but that looks like one of your front swaybar end-links (also referred to as the anti-roll bar end-link or stabilizer link).
The end-link connects your sway bar to your suspension arm or wheel knuckle. The sway bar somewhat connects the suspension on the left side of your car to the right side, which can reduce body roll while turning, or "stabilize" the car. If you've worked on your car before, you should be able to replace the end-link, although they can be a bit fussy to disconnect/reconnect. If your uncle can replace your wheel bearing, then he can replace the end-link.
The reason why it didn't really "matter" to your uncle is because your car doesn't need the swaybar to drive. It can improve handling in general, but it isn't an absolutely necessary component. However, as others have commented, you should get it fixed soon because it's not good to leave parts broken on your car, and the handling balance may be thrown off - it'll be biased towards oversteer now.