Cats can develop heart disease called cardiomyopathy. The most common form is caused by a thickening of the heart muscle (hypertrophic cardiomyopathy).
Unfortunately cats often hide this problem very well, and may show no symptoms until seriously ill. Your vet may be able to hear a heart murmur or irregular rhythm, which could indicate a problem. It is important to have regular check ups (at least yearly) so that your vet can check for problems like this. The best way to diagnose this disease is by ultrasound scan.
This video shows a normal cat heart on ultrasound scan. You can see the moving heart valves (mitral valves) of the left side of the heart towards the bottom of the picture. These valves are between the top chamber called the atrium and the bottom chamber called the ventricles.