"se" is a reflexive pronoun. The technical literal translation is "he does not feel himself well", but in English that sounds clunky. The reason is, we don't differentiate between "feel" as in your personal feelings and "feel" as in to touch/feel something. The object of what is being felt (either something else or yourself) is just implied in English, while in Spanish it is directly stated. "El no siente bien" would mean "he does not feel well", but in the sense that he's not good at touching/feeling things with his hands/feet/what have you, wheres "El no se siente bien" means "he does not feel well"in the sense that he's sick/in a bad state/etc.
in summary: se siente: he feels (as in personal feelings, "he feels good") siente: he feels (as in feeling some thing/object, "he feels the grass")
Yeah. In romance languages, you can't just treat a transitive verb like it's intransitive (e.g. "He smells the flower" vs "He smells"). You make the statement reflexive to accomplish the same thing (e.g. "He smells himself", or "The window breaks itself", etc.). In this case, "sentir" is transitive, so it must have an object, but the sentence is only about "him", so you use "se" (i.e. "himself"/"herself"/"itself").
The meaning may be the same, but the grammar is different. These are two different sentences in English: "does not feel" and "is not feeling" and they are two different sentences in Spanish also. You will learn how to construct "ing" verbs in Spanish in a future lesson, but the grammer used in this sentence does not follow the "ing" construction.
I personally am a bit confused with se, and whenever I read explanations they're always too confusing. The way I explain it, is that se is just saying "self" or "himself, herself, itself." So this sentence without se would be "He doesn't feel good," meaning physically feel, the sense feel. Putting se in is like saying "He doesn't feel good himself."
I Highly recommend checking out this link to help with this entire lesson:
Memorizing the reflexive pronouns ahead of time makes this exercise much easier.
I have an idea. Sometimes siente is a statement of empathy for another person's feelings. The literal translation "he does not himself feel well" expresses that His pain is all his own. I might be over-analyzing. I'll be glad when i fully grasp the usage of these pronouns