They are for keeping you warm mainly, also keep your shiney white shoes clean.
Mountain bikers don't realise the thought and time that goes into roadie fashion. They think that slapping on some ill fitting baggy items is "fashion". Roadies worry about colour co-ordination, keeping stuff shiney and even silly things like sock height etc. It's crazy.
Anyway, the guy had tights on and over shoes because he was out training and not trying hard so he didn't want to get cold. The best roadies will only take their tights off when riding if they're racing. It's very Euro to do so as well, so seen as cool.
When you reach roadie fitness, you'll be able to wear some warmer kit in summer and not raise a sweat.