"To me" is a typical way of introducing an opinion, in the sense "My understanding is . . .".
Sometimes, as in "To me it sounds . . .", "To me it means . . .", it could be interpreted as a fronted "prepositional object" of the verb, but I don't think it is necessarily understood in that way, and it is also used where that interpretation is not possible, as in "To me, the emphasis is on . . .".
To me, it is typical of fairly informal discussions of the sort you find on LEO, enabling one to distinguish between things one is stating as fact and things one is stating as opinion, sometimes a tentative opinion. It can also "soften" a firmly held conviction to avoid being confrontational when discussing something with someone who may hold a different opinion. I know I have used it on LEO, and I know I have sometimes changed it before hitting 'Submit' because it sounded "too idiomatic" when replying to non-native-speakers.
To me, it is typical of a rather British way of expressing oneself, though I am sure hm--us, for instance, uses it frequently.