There was quite a good video on the BBC News site which explained net neutrality in layman's terms -
it's here. I hope you can view this outside the UK.
I wouldn't be as sure as Kyle is that the US decision won't affect other countries. For example, in the UK internet delivery is protected under EU law but when we leave the EU? Who knows. We already have a bit of "preferential treatment" in the mobile phone market where some packages include more/faster streaming for a higher price but our main ISP services are protected not just by law but by the fact that the UK is one of the world's most competitive ISP markets. If a provider started to introduce higher pricing to access some sites over others there's enough competition to attract consumers elsewhere. Plus our laws regarding the physical provision of services, ie the phone wires and cabling, are both complex and competitive. So we have some leeway and probably a margin of advantage over countries where the basic provision isn't as protected, either by law or by market forces or both.
The USA isn't as protected by competition. It may seem strange but the country that regards itself as the bastion of free enterprise isn't really anything of the sort, not in this area anyway. A tiny number of media companies in the USA provide internet connectivity and they have carved up the market so that in many places consumers don't have much, if any, choice. As a result, if and when they decide to increase prices or to offer services such as Netflix or YouTube if and only if the consumer pays an additional fee then the consumer will have little choice there either. Net neutrality isn't just about sending all web traffic at the same speed, it's about doing that for the same toll-fee - which hitherto has been free.
I think there are potential problems in Australia, which doesn't have net neutrality laws and which has very little competition when it comes to service providers. If you live in a small town in Oz with only one telecoms company which can act as your ISP you already have very little choice, and because of the infrastructure the actual provision you get may be very poor; if they start strangling your streaming options for, say, video unless you pay more then you can choose to pay or not. But if ISP X decides to allow access only to Service A but not B and C because A is paying them megabucks to keep B and C out of the market, then you won't get any choice if ISP X is the only service provider in town.
I don't know where this leaves sites like FT although my guess is that it won't be affected much if at all. FT doesn't have a large footprint - it is almost entirely text-based with very few images and no video. I don't think it's the sort of site that the ISPs will expect to generate revenue for them and it would probably cost too much for them to try - in other words, the revenues they'd get wouldn't be worth the cost of billing.