Hi I'm new here and I'm a photographer so I figured I pay my way forward some by sharing what I know in a few threads.
The biggest thing that manual does is to let you control the "Holy Trinity" for photographers. ISO, Aperture, Shutter. When a camera is on automatic and you shot in low light rooms like restaurants or homes the images tend to be blurred if there is no flash.
Best thing you can do is learn a little about shutter speed. If you have manual on your camera then you will have a sports mode or TV mode.
Here are some basic speeds pros use.
To keep people from blurring in a social setting you can get away with a 1/100 shutter and sometimes slower. Dancing, think about 1/160 or so. Sports, 1/640 is dead minimum.
Water: To make it flow in a picture you shutter should be slower than 1/60 to make rapids freeze so you can see every drop 1/250 is the slowest.
If you learn a little about this then you can set your camera to TV mode. Learning this will kind of teach you some more things as well, but for a quick idea that is a big advantage I see in a camera that has manual mode. I see many blurred pictures from point and shoots and just setting it to TV and knowing how slow you can go can really help alot.