The role of Observer in Sehto is someone designated to track pokémon trainers during their gym circuit run to glean additional information about how they treat their pokémon and their attitude toward the practise of pokémon battling.
It's not a necessary role in the Sehto gym circuit setup, but it's appreciated if it exists, since it helps patch statements from affected pokémon and gym leaders together into a coherent whole, especially if the pokémon - as tends to be customary - spend much of the travel time confined to pokéballs.
Of course, the concepts has its downsides. For one, it's quite dangerous for the Observer, since it's normal that they're eventually discovered as the stalkers they are, and that hardly has to end purely in civilised discourse. For two, former attribute can serve as undue warning for the pokémon trainers - though Jagdish Tsukinaka for one isn't gravely concerned, given that he's happy if people stop the gym circuit regardless of their motivations. 'Creeped out because some guy has clearly been following us' is a perfectly legitimate reason to stop circuiting.
The current (and thus far only, as the role is a recent invention) Observer is Dakarai N'Sehla.