It may sound strange when talking about a "writer's voice" when what writers deal with are words, but it means the sound of the author's story. And defining it is very difficult.
On one level, it is how the writer uses dialogue, diction, punctuation, syntax and character development.
Dialogue – Do your characters talk a lot or are your chapters full of description of action or scenery. My characters talk a lot, so I keep running the risk of having "talking heads".
Punctuation – I love exclamations points and dashes !!!!! But I have learned to cut back on them. I read a book- have forgotten title – where there was little punctuation but many em dashes.
Diction – how do your characters speak - correct grammar vs street kid vs arrogant aristocrat
Syntax – how you follow the rules of grammar and speech. I've been known to bust a few rules. Sometimes I accept the corrections by my critique group and others times I stubbornly refuse.
Character Development – are your stories character driven or plot driven. If the people are more important then their personality must be explored.
I belong to a couple of critique groups and spend many hours editing my peers' work. I'm noticing that I can identify the author by the way it is written. How?
M writes YA and her characters speak "teenager". They can be sarcastic and flippant as teenagers often are. Her stories don't delve into teenage angst so she doesn't explore dark recesses of her characters thoughts, but there are still emotional issues. Her stories are fast paced and with a touch of joy and hope in them.
B has an intense sound. She writers erotic paranormal. Her characters - often the males - are dark and brooding. They usually have troubled/tortured pasts so she can dig deep and express their pain. The pace of B's stories is slower as the "erotic" sections build and ebb or as a character struggles through an emotional turmoil.
What about my voice? I don't know what i sound like, but I have a sense of it. When a cp (critique partner) suggests a change there are moments when my instinct/gut says the change is wrong. The cp's changes are how she would write that line. She can't help doing that - her voice is telling her how I wrote it isn't "correct." You have to learn to trust yourself as a writer to develop your style or else you could end up sounding like the six people who critiqued your work.
How to work on your voice? Write. Write. Write.
Write when you are really angry - steaming mad. Go back a couple of days later and look at what you wrote. Is it full of short sentences? Big words. Lots of exclamation points. Read what you wrote out loud . Do you sound like a pompous aristocrat or an angry drill sergeant.
Write about something that makes you very happy. Describe a kitten playing with a toy mouse. Write a letter to someone you love. And again, go back days later and look at your piece. Check your word choices, the length of your sentences and the number of adjectives. Read this one aloud. How does your physical voice differ than when reading the angry letter.
Now you are beginning to understand what your personal writing voice is.