This explanation might help you make more sense of it.
So your upload is 500kb. Think of that as how much data your internet connection can give the rest of the world.
In your example: Your slingbox, takes the show your TV provider is sending to your box and converts it to a more streamlined format (low bit rate etc) and broadcasts it to some place that is outside your house. That means it is using the upload bandwidth, so can only be sent at 500kb/s assuming there is no other traffic on your network.
That means that where ever you are viewing at (ie downloading content to), can only go as fast as the data is being given out (your upload speed at home). TSN's server, for example, probably has a bandwidth of many times what you have at home, say 10GB/s, so they can distribute content at that maximum rate, which means that if 1000 people are watching a clip, each person can download at 10mb/s, which is 20x what your home connection can provide for an upload.
I have no idea about what bandwidth is required for a decent slingbox feed, but I am assuming Google or your product documentation would have that info.
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