BBC, Channel 4 and Sky use a product called Kontiki to deliver content. It's a distributed delivery network (i.e. peer-to-peer, P2P). When you download a programme, it can come partially or entirely from a mix of seed servers, and other people such as yourself who already have part or the whole of the programme you're interested in. In other words, not only can you download programmes, but others can in turn download them from you. This is the outgoing traffic you see.
This reduces distribution costs for the BBC and moves them to ISPs whose users are accessing the content. In that sense, of course, it's no different to any other P2P network.
Unfortunately, Kontiki doesn't always play very nicely: by default, it tends to take all your available outgoing bandwidth, and it's got some issues with CPU time. Taking all your bandwidth, of course, is what gives others a good download experience, but it's as though the Kontiki default settings don't understand that, in general, outgoing bandwidth can less than one tenth of incoming bandwidth.
If you have a capped service which counts upload bytes as well as download bytes in your monthly limit, you could hit that limit in a day or so.
The obvious thing from a user perspective is to turn Kontiki off after downloading the programme (if you can). But this is against the spirit of the agreement you entered into when you installed the software.