Articles in portuguese, except in cases where they are simply usual, are used mainly to identify something.
If you say "gostam DE relógio", there's no identified watch, so, they like clocks (in general).
If you say "gostam DO relógio", there's an identified watch, so, they like THE one clock.
Read danmoller's comment above. "Do" and "da" are contractions meaning "of the" or "from the". Articles in Portuguese have the gender of the object noun so "do" = "de + o" and "da" = "de + a". "De" by itself means "of" or "from" and is used when you are speaking something in general rather than a specific object, person or thing.