what is på \sig? what is the meaning of these 2 words separated? how does the word wear gets builded up from these words?
På is a preposition and can mean "at", "on", "in", or other things, depending on the context. Sig is a reflexive pronoun; here it means "themselves", but in other contexts it can mean "himself", "herself", "itself", or "oneself". Att ha på sig literally means "to have on oneself" = to wear. Jag har på mig en jacka = I have on myself a jacket = I am wearing a jacket. Hope that helps some.
In Polish we also use this structure: "mieć na sobie" - (lit. to have on oneself) Though unlike in Swedish the reflexive pronoun "sobie" stays the same throughout all the pronouns, but the verb still conjugates according to it: Jag har på mig en jacka. - Mam na sobie kurtkę. Du har på dig en klänning. - Masz na sobie sukienkę.
Once again, "har på sig" is very similar to Polish "mieć na sobie" - "to have [sth] on oneself". :) Although in Polish you can also say "nosić" - "to wear". "Mieć na sobie" is usually used to describe a current situation.
Would this be appropriate for second person and first?
-- har på dig -- har på mig
What about "The women have on their dresses." That to me seems like a more literal translation.
Yes, it is wrong. The second "the" is not in the Swedish. So you should say "The women are wearing dresses" or "The women wear dresses".
hon har på sig = she has on (her)self = she is wearing
han har på sig = he has on (him)self = he is wearing
Sven har på sig = Sven has on himself = Sven is wearing
du har på dig = you have on yourself = you are wearing
jag har på mig = I have on myself = I am wearing
"sig" is third person; "dig" is second person; "mig" is first person
Note that the mig/dig/sig reflexive pronoun must match the jag/du/hon (har, etc.) subject pronoun or noun.
What is the difference between "the women are wearing dresses" and "the women wear dresses?"