"Voice", is a basic quality of writing, and like many basic qualities of writing, it is hard to describe and easy to recognize.
Although languages all differ from each other, they usually have constraints on how a sentence can be constructed, using rules of syntax and grammar. An author then has a limited amount of room to play in as to how they express themselves, unless they choose to establish a breaking of grammar rules as a trademark, or alternatively to just focus on bending the standard rules of grammar, such as by using involved sentences with multiple clauses, as a hallmark, such as in the work of the late, great, David Foster Wallace.
However, even while keeping themselves to a conventional level of writing, writers can develop their unique voice. However, just how this is done is hard to describe, and is indeed one of the mysteries of writing. For one thing, "voice" can not be taken alone, but is allied with the genre that the writer chooses to work in. To take a somewhat random example, Judith Krantz and Dave Barry have obviously distinct authorial voices, but that is tightly wound up with the fact that one is writing purple romances, and the other is a humor columnist. There are some very good writers who are not stylistically in possession of a distinct voice, and yet are still distinctive writers because they have an original form of plotting or character development.
Along with developing a distinct voice, often writers have to learn how to muffle their voice. Most journalists are taught to not let their writing get in the way of the story, and have to rely on strict style guides to tell them how to write. That is why any given New York Times article sounds like any other New York Times article.
Another issue is that the voice in a piece of fiction can be the author's voice, or it can be the voice of the characters speaking, or even the voice of a narrator who is somewhat separate from the author. For example, in The Lord of the Rings, the narrator and the character's voice is very medieval and somewhat austere, which is actually not all that similar to Professor Tolkien's normal voice, which was fairly modern. To be able to create multiple voices is the sign of an accomplished and skillful author.