The singular, "ubranie," is neutral; however, this form ("moje ubrania") is actually plural.
The possessive just has to agree with the case. Here it's just a phrase, so it's Nominative.
If it was Genitive, for example, that would be "moich ubrań".
The word "ubranie" basically means one set of clothes. For example the clothes I am wearing at the moment, the clothes I put on my chair to wear tomorrow, some elegant clothes to wear on special occasions, etc.