This has to do with the speed of the connection he's getting from his internet provider. When the provider quotes a number for speed, they're giving the upper number, or the fastest it could be. DSL, in Leo's experience, is generally more consistent than cable internet, though. Some internet providers have a little trick they use called "burst mode", which means they give real fast internet when first connecting, but then slows down. Leo says he could call AT&T and go a tier higher in internet speed, which would cost around $10 a month more.
In order to stream content live, Tim would have to have sufficient connectivity (which isn't necessarily the same as internet speed) to get the packets that are coming to him. All of this streaming data is grouped into packets, so a chunk of the video comes, and then another chunk and so on. He'll have to get it in a timely enough fashion for it to be in order and play back. There's a number of strategies to accomodate the fact that the internet is inconsistent.