Sort of. Megapixels are a measure of resolution, which is essentially how many mini-dots of color make up an image. One megapixel is the equivalent of 1,000,000 of those little dots, called pixels. They make up every digital screen you've ever seen. The more pixels an image has, the more detailed, and the the clearer it can be.
Now, there are some issues with large amounts of pixels in a small camera. One is that each pixel in the sensor must capture light, and the smaller they are, the longer they take to capture enough light for a well-lit, clear picture. That leads to the second main issue, which is blur. When the shutter time (amount of time that the camera sensor takes in the light that forms the picture) is long, you get a well lit, clear picture... provided the subject is stable, and your hand is too. If something moves, then the sensors see it both in it's initial - "true" - position, and every position in between where it ends up when your sensors stop taking in light. This causes blur. When the shutter time is short, blur is reduced, but pictures are darker.
So, yeah, the software you use is important. Some will use smart software to correct for blur, some will automatically brighten the image (Which reduces detail), and the best ones (IMO) let you set your own shutter time depending on what you're taking a picture of. For example, if you're watching a baseball game outside, you should set a very short shutter speed so that you minimize the amount of motion blur captured, but there should be plenty of natural light provided by the sun. If you're in a dim art gallery, you may want a longer shutter time, as you need the time for lighting, and nothing's going to be moving.