As an Ex silver player and gold for 2 seasons now. The skill difference is actually quite noticeable. Here's a few to give you a general idea:
1: Gold V and Silver I aren't much different, Anything else is huge.
2: Golds have a better understanding of things, CS, wards, jungle routes, ECT. Silvers aren't very good at last hitting, most don't know where wards go let alone what they are (Hence the meme of only supports should buy wards), Silver junglers are more or less similar to bronze junglers, in which I mean they will lose their mind if they don't get something from a gank they make and you will never hear the end of it from them "I'm never ganking your lane again" sound familiar?
3: 60% of players are silver/bronze. 20% are gold and the other 20% are plat+ (This is a rough estimate based on silver/bronze alone)
4: It's not that we actively think we're better than silver players, it's that if we've played with you before and have seen how you play, it's that we know it just won't work out. We know your play style, we know your bad habits, we've probably talked about it to you before hand: EX of this would be a cait I recently had in a game where she was silver IV and told me "My builds from moba fire, so I don't care what you tell me to build, mines right"
There's others, but this post is already a TL;DR. But hopefully this gives you some form of understanding.