While you are dreaming, your body undergoes noticeable changes. Your adrenaline rises, your blood pressure increases, and you heart beats faster. Given this hyperactivity, it should be no surprise how someone with a weak heart can die in their sleep. Their heart may not be able to withstand the strain and the erratic changes that their body is going through.
Dreaming takes place during REM, which stands for Rapid Eye Movement. It is thus called, because your eyes move rapidly back and forth under the eyelids. REM sleep takes place in the fourth stage of sleep and accounts for 15-20% of your sleep time. From the point you fall asleep, it takes 30 to 90 minutes before you start dreaming. You cycle through the 4 stages of sleep and may enter the REM stage 4 to 7 times in one night. During REM, your blood pressure and heart rate fluctuate and increase. It sounds like your body is going through a lot, but in fact, it is quite the contrary. During REM, your bodies are completely immobile and your muscles remain completely relaxed. You may shift in your bed throughout the night, but when in REM, you are completely still. This is commonly known as "REM Paralysis".
In REM sleep, the mind is as active as it is during waking. However, chemically it is different. REM is controlled by the excitability level of the cholinergic neruons. Noradrenaline and seratonin are missing in the brain when in the dream state. These chemicals allow the brain to carry out task, solve problems and remember things. This is a reason why you find it so hard to remember your dreams.