Translation:Miikka, what kind of apartment do you have?
It commonly refers to an apartment, as the translation suggests. Since you're asking, perhaps the UK English term "flat" is more familiar to you. Although it can also be any type of residence, since it literally means something along the lines of "place where one lives".
Joo, ei. :) "Sinulla" is "sinä" + "-llA, which combined with "on" (is) means "you have".
"minulla on" - I have
"hänellä on" - s/he has
"meillä on" - we have
"teillä on" - you have
"heillä on" - they have
"koiralla on" - the dog has
However, the -llA (adessive) ending is used to indicate e.g. that something is on something else, so if you see the -llA ending that isn't a sure indicator of a possessive construction.
"pöydällä on" - on the table is
"katolla on" - on the roof is
"Kissa on pöydällä/Pöydällä on kissa" - there's a cat on the table
If you wanted to express that something's on you, the dog etc. you could use the word "päällä" (on top of), which you can also use with words such as "pöytä" etc.
"Päälläni on koira" - there's a dog on (top of) me
"Pöydän päällä on kissa" - there's a cat on (top of) the table
The adessive is also used in the following construction (as well as in many others):
"Tavataan asunnolla/talolla" - let's meet at the apartment/house