Since I like singing opera, I sing “Nella fantasia” but I always wondered what does nella mean in this phrase? I know that fantasia means “fantasy”.
"Nella" is the contraction of the preposition "in" and the article "la":
"in" + "la" = "nella".
For other contractions of Italian prepositions with articles, you can see this.
Even if what other people have answered is true, the translation is not correct. That depends on the fact that this is a irregular construct. Generally speaking "Nella" means in + la, so it translates to in + the. Nella casa = In the house. In this case, though, it doesn't mean in the fantasy, it means In Fantasy; it can also be translated with In fantasies. The closest translation, though, is probably In Dreams, as Fantasy in English has a stronger "Something I can think of, but won't happen" connotation, in Italian, in this contest, it's closer to "Something dreamy I really wish it would happen, whether it will or not".