The law is incredibly simple.
If you run a network or a website, and someone uses it to do something bad, you are not liable for it (with exception). Websites that editorialize (newspapers) are still liable. This is why Hulk Hogan can sue Buzzfeed, but Vordrak can't sue the Kiwi Farms.
What Trump is threatening to do to hurt Twitter is repeal this law, so if someone uses Twitter to do something bad, Twitter is liable for it. He is trying to 'clarify' the law so that deleting tweets and banning accounts is editorialization. Repealing the law in its entirety makes everyone personally, civilly liable for anything published on their platform.
Notice how what he's threatening to do doesn't actually solve the problem. It just makes these platforms so liable for what they publish that the only solution is to censor even more. Any defamation complaint would mean tweets and videos would have to go down. If someone posts something here and I get a complaint it's defamatory, I have to delete it or accept liability.
Currently, the process is: Person goes to court, gets court order to remove content, content is removed. The impetus is on the person to go to court.
Contrast that with the DMCA. Section 230 explicitly does not cover IP. So when I get a DMCA complaint, and I tell them to fuck off, I actually am personally accepting responsibility for that content. Every time I do this I evaluate the use of the work and decide if it's fair or not. This is me sticking my neck out on behalf of users.
(2) No effect on intellectual property law
Nothing in this section shall be construed to limit or expand any law pertaining to intellectual property.
I can't do that for statements. Every time someone claims a post is defamation, I have to evaluate the facts and determine if I trust those claims so much that I believe I can personally represent it in court on behalf of the person making the post.
To anyone who would say "you're in Serbia, why do you care?" my answer is: I am physically in Serbia, but my possessions are not. Verisign, the company that leases all .NET domains, is American. My bank accounts are American (and thanks to the USA PATRIOT Act, unregulated banks like Swiss banks do not allow Americans to have accounts with them). My hardware is in the US. My datacenter is in the US. My LLCs are American. A civil judgement against me means they can take all of that, including the domain, Few other countries have the strong and broad protections for both speech and services as the US does currently.
Repealing Section 230 does not just spite Twitter. It emboldens Twitter to censor as hard as possible and jeopardizes any small forum without financial resources. I cannot become an outlaw for the forum. I cannot throw away my American citizenship for the forum. I've already done enough, and with the way Trump supporters are cheering this on, I don't even want to even bother.