Well the idea is that anyone can run for election and in order to afford to do so people can pool their resources and help out. So if I want to run for mayor and you really like me a lot better than the other person you can pitch in in different ways. You can help me reach out to voters, you can make calls for me, you can help me with social media, or you can donate money to me so I can pay people to do those things. This by itself really isn't a problem especially when there are caps on how much money people can donate, which there are. But if you donate as much money to my campaign as you are allowed what's to stop you from calling up the local TV station and paying them directly to run an ad for me? I might not even necessarily be involved at any point.

The big problems come when we do things like decide a multinational corporation qualifies as a person and therefor the rules around how much money a company can donate don't apply to them. And we do things like change the rules around what the limits are. And then people do things like fund PACs where they pool their resources and promote a candidate on their own without actually donating to the campaign itself directly. Some of these are just outright stupid decisions that never should have happened in the first place and others are loopholes. Campaign finance reform in the US doesn't have a single silver bullet that's going to fix everything. There's a lot of things that are wrong with it. Citizens United (the corporate personhood ruling) is probably the biggest but it's still just one problem among many.