Roaming is when in your travels to call, text or connect to the internet you have to use a tower that is owned by a provider other than the one you have a contract with (you have roamed into an area where your provider can't provide you service but another network can). Providers have made deals to allow this but when you do the provider you connect to will charge you more than their customers and likely more than your service provider would if they owned the tower. The non-contracted provider doesn't bill you though, it will bill your provider who will pass on the cost to you on its monthly statement, maybe with a hidden additional "service fee" of its own.
In the US the major providers have built up extensive nation-wide networks since those early days so you may never see roaming charges since you are generally using your network's towers. This isn't the case when you travel to another country. The deals your provider has made overseas with other companies can cost you a lot on your monthly bill. You may not see the costs broken down like Mint Mobile does (see post #7 above) but your provider figures something out to cover the costs you and others incur, perhaps by figuring an average cost of what users incur in country X. For example, data connection might not cost you any extra but to do that your provider and their contracted provider in country X may have to restrict your speeds.
So, when in another country, if you get service at all you end up paying more for it (e.g. price per call minute) and/or having service deprecation (e.g., restrictions on number of calls or texts or slower data speeds). One US provider might give you the same deal as you get at home but to cover their costs they may charge you X amount per month service charge or perhaps Y amount for every day you connect to one of their overseas partners.
The EU has put restrictions on companies so that service charges between EU providers essentially will mean no or essentially little extra charges for roaming. I think this takes effect in July 2022.