A midline incision is used for a number of surgeries. As you've surmised, one possibility is for a tummy tuck (abdominoplasty). This procedure often employs just a transverse (horizontal) incision, but a small longitudinal (vertical) incision may also be used if a larger amount of tissue is removed. Very large removals of tissue may result in a midline incision running all the way from the pubic hairline to the bottom of the breastbone.
The most common type of Caesarian section involves a transverse cut, but it was not always thus. A longitudinal midline cut was once the incision of choice for the C-section, and it is still used on rare occasions.
A midline incision may also be used to perform an exploratory laparotomy--it gives good access to most of the abdominal organs. In recent years and in countries with good access to modern medical equipment, such exploration is now much more likely to be conducted laparoscopically, using a camera inserted through a small incision. Larger incisions are still used even in North America if a problem is discovered that cannot be readily treated laparoscopically and in cases (trauma, etc.) that require rapid, open access to the abdominal cavity.
/I am not a real doctor
//I play one on the internet