What is a fistula? can one get rid of it without a surgery?

When I saw the question, I assumed you were talking about a fistula that occurs in cleft palates, but from reading the other answers I can see that it might be regarding a different type. Can you give a little more information? The other answers were really thorough, but it still might help to know more.

In medicine, a fistula (pl. fistulas or fistulae) is an abnormal connection or passageway between organs or vessels that normally do not connect.

Various types of fistulas include:

Blind: with only one open end
Complete: with both external and internal openings
Incomplete: a fistula with an external skin opening, which does not connect to any internal organ
Although most fistulas are in forms of a tube, some can also have multiple branches.


Causes
Various causes of fistula are:

Diseases: Inflammatory bowel diseases, such as Crohn's disease and ulcerative colitis, are the leading causes of anorectal, enteroenteral, and enterocutaneous fistulas. A person with severe stage-3 hidradenitis suppurativa will also develop fistulas.
Medical treatment: Complications from gallbladder surgery can lead to biliary fistula. Radiation therapy can lead to vesicovaginal fistula. An arteriovenous fistula can be deliberately created, as described below in theraputic use.
Trauma: Head trauma can lead to perilymph fistulas, whereas trauma to other parts of the body can cause arteriovenous fistulas. Obstructed labor can lead to vesicovaginal and rectovaginal fistulas. Vesicovaginal and rectovaginal fistulas may also be caused by rape, in particular gang rape, as evidenced by the abnormally high number of women in conflict areas who have suffered fistulae.

Treatment for fistulae varies depending on the cause and extent of the fistula, but often involves surgical intervention combined with antibiotic therapy.

Typically the first step in treating a fistula is an examination by a doctor to determine the extent and "path" that the fistula takes through the tissue.

In some cases the fistula is temporary covered, for example a fistula caused by cleft palate is often treated with a palatal obturator to delay the need for surgery to a more apropiate age.

Surgery is often required to assure adequate drainage of the fistula (so that pus may escape without forming an abscess). Various surgical procedures are commonly used, most commonly fistulotomy, placement of a seton (a cord that is passed through the path of the fistula to keep it open for draining), or an endorectal flap procedure (where healthy tissue is pulled over the internal side of the fistula to keep feces or other material from reinfecting the channel). Treatments involving filling the fistula with fibrin glue or plugging it with plugs made of porcine small intestine submucosa have also been explored in recent years, with variable success. Surgery for anorectal fistulae is not without side effects, including recurrence, reinfection, and incontinence.

It is important to note that surgical treatment of a fistula without diagnosis or management of the underlying condition, if any, is not recommended. For example, surgical treatment of fistulae in Crohn's disease can be effective, but if the Crohn's disease itself is not treated, the rate of recurrence of fistula is very high (well above 50%).


Theraputic use
In end stage renal failure patients, a cimino fistula is often deliberately created in the arm by means of a short day surgery in order to permit easier withdrawal of blood for hemodialysis.

Fistula: An abnormal passageway in the body. The fistula may go from the body surface into a blindpouch or into an internal organ or go between two internal organs.

For a common example, an anal fistula has an opening in the skin near the anus that leads into a blind pouch or may connect through a tunnel with the rectal canal.

For a rare example, a gastropericardial fistula is a passageway between the stomach and the pericardial sac (that surrounds the heart).

There are numerous types of fistulas or (if you like the proper Latin plural) fistula. They are usually designated by the organs or parts they connect (anovaginal, bronchoesophageal, etc.).
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Since by definition, they are not normal, usually do not serve a purpose, and can cause problems, the most common medical recommendation is surgical repair. The best thing to do is get your doctor to examine your type of fistula, get all the ultrasounds, xrays and studies, and present you with other options that you can choose.

An opening in the body, usually in the circulatory or airway systems, that exists where one shouldn't. To the best of my knowledge, surgery is currently the only way to correct one.