A place that's cramped is uncomfortably small or crowded, like a cramped elevator with one too many riders or a cramped subway car at rush hour.
This adjective comes from the verb cramp, "to restrict." When you're in a cramped situation, your movement is restricted in some way, often because there are too many people standing too close together, or simply because the space is too small. You might have a bedroom all to yourself, but if it's the size of a closet, you'll still feel cramped in there.