In this context, I would say "awkward" means that your sentence is grammatically correct but not idiomatic. It is not wrong but it is not what a native speaker would say in this situation.
In the case of the two sentences you have given, there is a difference in meaning. "I like apples." = You like this fruit. You like eating them; maybe you like their appearance. A general statement.
"I like an apple." This requires a context. You might say this in answer to someone or in the course of a conversation about which fruit you like to take in your packed lunch.
The difference is slight, but obvious to a native speaker.
I hope that helps.