There are many things that can make a difference in the way your instrument sounds. These include: new strings, a better bow, soundpost adjustments . . . even what type of bridge, or the chinrest/shoulder rest you use, or the number of tuners you have. I'll start at the end and work my way backwards with some educational tidbits about each of the above.
Every violinist, even a brand new one, should know the difference between tuners and pegs. Pegs make the big adjustments in pitch. Fine tuners, which make the "fine" (or small) adjustments, are certainly convenient. But beginners don't always know that the tuners may not always eventually be necessary. The rationale behind having four fine tuners is that it makes it easier to train a beginning violinist to tune. The rationale behind gradually reducing the number of tuners, usually after you're very comfortable using the pegs and when you get to a full-size violin (until you're left with only the E string tuner, or even no fine tuners at all) is that any type of extra hardware on the instrument impedes the purity of tone of the violin.
The chinrest, which can come in many styles (center-mount, flat, etc.), ought to be comfortable, and combined with the shoulder rest, be at the optimal height for the player to have excellent and secure posture. I often remind my private students that everything we do in terms of posture has a direct impact on the technique, and thus the sound, we produce. Perhaps of interest: I recently learned from another excellent teacher/violinist who studied this that if your violin sits too far on your shoulder to the left, or too far off your shoulder to the right, your brain will tend to favor the hand on that side of your body. I realized when she told me that, that my violin was sitting very much on my shoulder, partly due to the curvature of my shoulder rest. And I indeed have been much better with my left hand, traditionally (which controls intonation and some rhythm), than I have been with my right (which controls articulation, tone, rhythm and dynamics). I often hear whether or not something is out of tune before I hear anything else, because that's where my focus--and as a result, strength--lies! After hearing this interesting bit of science, I bought a different shoulder rest that allowed me to shift the violin slightly towards the center of my body (while having the violin remain parallel to the floor, of course), and it made a difference! I was suddenly more aware of what both hands were doing at once, and I could more easily and more quickly shift my attention back and forth between the two. It seems to have made a difference! I do believe my articulation (from the right side/hand) has become more strong and clear after that adjustment.
The bridge can make a difference. Many years ago, a luthier offered to make a new bridge for my recently-purchased French violin. He noticed my f-holes were farther apart than most of the violins he was familiar with and determined the instrument called for a wider bridge than normal. As a result, I played with a specially carved viola bridge he made for my violin for a very long time. But it affected the sound in interesting ways. I often felt that I had a microphone under my strings, even when playing sul tasto. It was very difficult to blend with those around me! Part of it was the instrument itself, but it still seemed slightly unnatural, and I suspected it might have something to do with my unusual bridge. This luthier was a good friend of mine. His unique bridge was sentimental to me and I didn't have the heart to change it. When I finally had the courage to talk to someone who was able to adjust my original violin bridge, which I had kept over the years, and fit it back on my violin, as well as create a new soundpost, I was pleased to discover some welcome differences in the tone. Not only did I have a larger dynamic range (including soft), but it was a warmer sound, more focused, and playing octaves in tune was much easier! Playability in an instrument, as well as sound, is important!
To move on up the list, let's address the bow. It's helpful to remember that the bow is half the instrument! When you've reached your violin's limit for how helpful it is in making you sound your best--when it's holding you back and you're ready for an upgrade--but you don't have the money for a new violin, never fear! A great way to upgrade your stringed instrument is to upgrade your bow! A good rule of thumb is to have a bow that's worth at least 10% of the value of the violin. That's a minimum. If your violin is only $700, you may want to up that percentage and get a bow that's $100-$200 when you're ready to make improvements.
And finally, I recommend changing your strings at least once every two years if you're a new violinist. Change them every year if you play for a couple of hours a day. Every three-to-six months if you're in a professional symphony. Also, I learned firsthand recently that if you are doing a lot of solo playing, for example, with an orchestra behind you, rather than ensemble playing, you will wear out your strings faster. It makes sense. You have to produce more sound to carry over a full ensemble, so you're naturally harder on your strings! You don't have to wait until your strings are false or unraveling or broken. After a while, strings will just start to sound dull. Switch them out on a regular basis, saving the old ones as backup strings in case one does break, kind of like having a spare tire on hand for your car. Every year, I know I'm probably going to get new violin strings from my husband whenever my birthday rolls around. I love the sound of new strings! They sound very bright and resonant for about two weeks after you put them on. Experiment with different brands. Even different brands at one time. Each type will make your violin sound different. Different websites exist with string comparison charts on them, that tell you where a certain brand of string falls on the spectrum of warm, bright, etc. I currently have strings from three different brands on my violin--one brand for the E, another for the A and D, and a third type for my G. When changing your strings out, it's wise to change all your strings in one sitting. But make sure your bridge doesn't fall over in the process! In other words, don't take off all the old strings at once before putting on the new ones. Take one off, replace that one, then move to the next. And don't go in order. If you start with replacing the A, for instance, skip a string and do the G next, then the E, etc., eyeing your bridge the entire time.
I worked for two luthiers and other music stores. You tend to pick things up over the years. I hope you learned something new in this post!