The brain is protected by the skull and is very delicate. Opening the skull to look at living brain tissue is dangerous, and cutting into the brain can damage it. Scanning lets doctors investigate the brain from the outside without surgery.
A CT scan passes X-rays through the head from many different angles. A computer combines the readings to build up detailed slices of the brain. This shows its structure, so doctors can find a tumour, a bleed or physical damage.
A PET scan shows function. The patient is injected with a radioactive tracer, usually attached to glucose. Active parts of the brain use more glucose, so more tracer collects there. Detectors pick up the radiation given off, and a computer shows which regions are most active, for example while the patient is speaking or thinking.
Both methods are non-invasive, but both expose the patient to some radiation, so they are only used when the benefit outweighs the risk.