The benefits are:

Minimal tissue handling and hence reduces the risk of adhesions.
Saline irrigation is constantly done during the procedure to prevent drying of tissues and blood clots from sticking to the tissues.
Meticulous control of bleeding is done hence, less blood loss.
Adhesion prevention barrier such as the Adept solution or Interceed is used to prevent scarring of tissues.
Recovery stage is short and hence the hospital stay is reduced to 24- 48 hrs.

Prior to fibroid removal surgery procedure, the surgeon might give hormonal injections to reduce the size of the fibroids to make the procedure easier to perform.

The surgeon will make a couple of tiny incisions in the patient's lower abdomen. Normally, 3 or 4 small incisions are made on the abdomen depending on the uterine size and other circumstances. The surgeon will make a 12mm incision within the umbilicus and the remaining incisions are made smaller, around 5mm.

A tube or a small needle is first inserted through one of the incisions to fill carbon dioxide in the abdomen to inflate the patient's abdomen. This helps to keep the abdominal wall away from other internal organs reducing the risk of injury and also helps the surgeon to see well.

The surgeon will then insert the laparoscope through the small incision made in the navel, which will transmit images to a screen that will help the surgeon see inside. The surgeon will use a morcellator, a special device used to cut the fibroid into smaller pieces, which are then extracted out through a smaller incision. At the end of the procedure, all instruments are removed carefully and the incisions are closed with stitches.

Myomectomy has a lower complication rate but in rare cases, the procedure poses a certain set of risks

Excessive blood loss : The surgeons take great care and employ extra measures to prevent excessive bleeding, including blocking flow from the uterine arteries and injecting medications around the fibroids to cause blood vessels to clamp down. The blood loss is higher with a larger uterus so medicines are given to reduce or shrink the uterus.
Scar tissue : Incisions into the uterus to remove fibroids may lead to adhesions resulting in bands of scar tissue that may develop after surgery.
Pregnancy or childbirth complications : A myomectomy can increase risks during pregnancy and delivery often resulting in a C-section to avoid rupture of the uterus during labor.
Rare chance of hysterectomy : The surgeon might have to remove the uterus if the bleeding is uncontrollable or when other abnormalities or complications are found during the procedure. This occurs on very rare occasions.
Rare chance of spreading cancerous tumor : There might be a rare chance where a might be mistaken for a fibroid and by cutting it into pieces may lead to the spread of cancer.