You have choosen a tricky one there. It's a complex verb and a complex structure.
According to the D.R.A.E
dar
22. tr. Hacer sufrir un golpe o daño. Dar un bofetón, un tiro. U. t. c. intr. Dar DE bofetones, DE palos.
...
49. prnl. Dicho de una cosa: Suceder, existir, determinar.
Se da el caso. En circunstancias dadas.
In
Se me da bien
we've got the 49 meaning. prnl indicates that it's a pronominal verb
The grammatical term "pronominal" means "relating to a pronoun," so
pronominal verbs require a reflexive pronoun. They’re often
incorrectly referred to as reflexive verbs, when in fact the latter
are just one type of pronominal verb. The defining characteristic of
pronominal verbs is that their subjects are acting upon themselves.
Pronominal verbs are much more common in Spanish than in English.
What sets pronominal verbs apart from non-pronominal verbs is that
pronominals must be conjugated with a reflexive pronoun, which
always agrees with the subject. {source}
As noted in this text - originally in Spanish -
se - Es un morfema al servicio exclusivo de la significación del
verbo; forma parte del verbo - verbo pronominal - y juntamente con él
constituye el núcleo del predicado. Su supresión es imposible o cambia
el significado del verbo.
[English] se - It's a morpheme exclusively related to the verb
meaning; it's a part of the verb - verbo pronominal - and them both
form the nucleus of the predicate. It's removal is not possible
because it may change the meaning of the verb.
As stated above, if you have just
Me da bien
then you got a different meaning. Probably 22 [see D.R.A.E above] in its intr [intransitive] meaning because there is no object in that phrase, it's not the usual "dar/give" meaning because nothing is being given explicitly. That sentence lacks information, it's not complete for a native speaker. I tend to fill it in my head as Me da bien [para el pelo], an idiom.
The most accurate translation of: I'm good at it
in Spanish is: (Yo) soy bueno en ello
Notice that it's practically a word-by-word translation. It seems that you're trying to compare "I'm good at it" with "Se me da bien", two completely different phrases. They've got practically the same meaning but they are constructed differently. In the Spanish version the subject is it, the thing that I master, and that subject is omitted while the subject in the English version is I and the pronoun it is present as a complement.
Let's reorder the phrase: (Ello) dáseme bien
where
(Ello) - it - subject omitted
dáse - verb
me (a mí) - to me
bien - well
This reordered version is percieved as archaic, it's more or less how Spanish were spoken centurys ago but you can see that all the elements are present in your original version.
I've not found an idiomatic version in English, it should be something like it's my forte (suggested by Mv Log in the English Learners Site)
it - subject
is - verb
my - particle that establish the relation with me
forte - positive characteristic
Hope all this text helps you to understand the sentence.