An MRI machine uses a huge electromagnet to surround your body with a magnetic field. The body makes disturbances in that magnetic field that are picked up by the computer. The computer makes very detailed pictures of the brain that are printed on film for the doctor to keep.
An MRA is a Magnetic Resonance Arteriogram, a picture of the blood vessels in the brain made by an MRI machine. It takes longer than a regular MRI. People with some kinds of epilepsy have some abnormal tangles of blood vessels in their brains. These blood vessels sometimes leak and can injure the cells around them, causing seizures. It's important to find blood vessel problems early so they can be taken care of before they cause a stroke.
This is a picture of an MRI machine and the computer that runs it. (This is not the one that kept breaking down when I had my MRI!) Photo courtesy of Florida Spine Institute.