According to my teacher, my essays are too stilted. How can improve my writing style and also how can I "write with purpose"?
I really admire you for taking the constructive criticism from your teacher and trying to improve in those areas. That is a mature approach to writing (to anything, really); and, since you're starting in ninth grade, I'm confident you will be a supremely effective writer by the time you graduate, if not before.
I can't know for sure, but I think what your teacher is trying to say is that your essays don't reflect your authentic voice--they don't sound like you. "Voice" is what makes your writing sound like you. It's a little hard to explain; however, once you get a feel for writing in your own voice, you'll find it is the easiest part of writing.
Consider this. If you were to read just one of the questions I've answered for eNotes, you would not really have a good idea what my writing voice "sounds" like; if, however, you were to read fifty of them, you would probably be able to pick my answers out based on my sentences structures, vocabulary, use of punctuation, transitions, and many other things. In general, I don't really think about those things, I just do them because they are comfortable to me.
The same thing is true with my students' essays. After I read a few rounds of essays, I can usually "hear" the things that tell me who wrote them (probably much like your teacher can). If I can't do that, one of two things is happening. First, the student may be trying too hard to write what he thinks I want to hear (often very stilted and overly formal), or the student simply hasn't yet found his consistent voice. Both problems are correctable.
I'm guessing, based on the wording of your question, that you are perhaps the former, writing more formally than is necessary. Your natural writing voice may be more formal than others, but I suspect you could comfortably "relax" your writing a bit and still be true to your voice.
Here are a few more things to consider. If you find yourself grasping for a more eloquent or formal-sounding word instead of using the best word you naturally think of, you are not writing in your natural voice. If you work and re-work sentences in order to sound more like what you think sounds more scholarly or sophisticated, you are actually stifling your own writing voice. If you do not have a clear organization, direction, or audience in mind, you are probably just writing, not writing with purpose.
None of these things is inherently bad; in fact, finding just the right word and working on a sentence until it is just right are admirable and worthwhile efforts. Just change your thinking a bit so that you pick the best word you would naturally use, rewrite a sentence in the best way you would say it, and make sure you have something to say and your readers can follow you.
Purposeful writing is focused writing: no rambling, no wordiness which does not move your ideas or arguments forward, clear organization, and consistent markers (transitions) to make sure your readers are able to follow you. The best advice I can give you is to be yourself when you write and make sure you have something to say.
The link I attached below (though it is directed at bloggers) gives a few specific and excellent ideas to help you find your voice if you're struggling.
In short, effective writing should be a reflection of you, so make your voice heard by using the vocabulary and rhythms which come naturally to you and then putting them in a form which your readers can understand and appreciate.
Here are some other thoughts, merely supplementary to all the constructive ones already posted:
Although we strive for originality, we first learn by imitation, sometimes inadvertently, as with former Latin students who unconsciously employ participial phrases in their writing at the beginning of sentences from conditioning [too, too many translations of Julius Caesar's writings--at least they are good for something]. At any rate, reading many of one favorite author's works (classic works) will give a student a sense of that ine author's style, also, there may be phrases, sentences, words, etc. that the student wishes to imitate in structure. Reading, reading, is important as it is nothing more than the reverse side of writing, is it not?
"Reading maketh a man full," Thomas Jefferson wrote.
Read poetry, too, because poets select precise words, words with lovely nuances, words with emotion, words with intensity. Learn words because then inclinations for certain words will make them more yours than others that you may sporadically apply. Become a logophile! When you write, then, you will begin to put something of yourself into what you write. Don't be afraid to use an evocative word as this will connect you to the page as well as invite the reader into your "secret" that you are gradually revealing. Try to write in such a way that you invite the curiosity of your reader.
Talk about what you write with others. Exchanging ideas, bouncing them around, so to speak, lets you discard ones that are not worthy and snatch those that are. Practice, practice, practice. The more you write, the better you will become.
Above all, your genuine interest in wanting to write well is a big step towards success. Bravo!