Why cant it be "Ti lidé se na stromy dívají"
It can, but only when STRONGLY stressing dívají.
The people are LOOKING at trees. or The people ARE looking at trees.
I will add it because Duolingo is not a good place to enforce natural Czech word order. You have to learn it by other means anyway.
Why do you need 'se' with some verbs?
Because the language works that way. The historical evolution caused it.
What meaning does it have in the sentence, though?
You can read about reflexive verbs in James Naughton's Czech - An Essential Grammar, section 7.3. You should be able to find it easily and download it for free.