Good question! It does not really mean much, "på" is just a general preposition to tie verb and indirect object together. Adding a "på" in this case emphasises the tasting process.
So could the sentence still be grammatically correct without "på"?
Thank you for your reply! But I'm still a bit confused. What would be a situation where this phrase could/should be used instead of 'jeg har smakt maten'?
It's a fine nuance. "Smake på" would be used especially when you are tasting to see wether it is good or not, as a test. While simply "smake" could be used any time. For example if you say "Har du smakt på maten? Trenger den mer salt?" the emphasis would be on the testing of taste. Or if you're at a restaurant, and you already have your food in front of you, you could ask your neighbour "Har du smakt på maten ennå?" - have you tasted the food yet. That would be an indirect question whether the food is good or not. But if you are referring to some other visit to the same restaurant, and were saying "Jeg har smakt på maten her." it would sound like you have been there and been going around tasting different kinds of food at thestaurant.
I'm still a bit of a norwegian n00b but maybe it emphasizes that the person speaking has only tasted a small bit?
I translated this as "I have tasted of the food", but that was shot down. Since there's a subtle difference between "to taste" (usually means to experience the taste of) and "to taste of" (means to try a little bit of and see how it tastes) in English, I wondered: can "smaker" only have the former meaning?
The emphasis would be more on testing the food than how much. I'm not a native English speaker, but I have never heard "to taste of". Is that a common phrasing?
I know zero Norwegian, but I'm a native English speaker. Trying a little of something to see how it tastes is most often phrased with "taste" as a noun: "I had just a taste of your wonderful recipe". As a verb, "to taste of" is indeed used, but less often as LBoksha suggested it. His "I have tasted of the food" represents a kind of shortened form for "I have tasted some of the food", and has a slightly antiquated, literary, or poetical feel to it. One could say "It tastes of cinnamon just a bit." though, and be quite ordinary, indicating a food that one has tasted has a bit of flavor from a particular ingredient, or something like it - a hint of flavoring.
Thanks. I've heard the form "It tastes of <aromatic substance>" many times before, but never in the more active form, as "I have tasted of the food".