The heart is an amazing pump. For decades, it reliably and safely pumps blood. Just as the heart is a pump, the blood vessels are pipes. They take the output (blood) from the pump and distribute it throughout the body. Blood pressure measurements are simply a way to keep track of the performance of that pump and those pipes.
Two numbers make up a blood pressure reading: systolic and diastolic. A typical reading might be 120/80. When a doctor puts the cuff around an arm and pumps it up, what he or she is doing is using the pressure exerted by the cuff to cut off the blood flow. As the cuff's pressure is released, blood resumes flowing and the doctor can hear that flow through the stethoscope. The number at which blood starts flowing (in this case 120) is the measure of the heart's maximum output pressure (systolic reading). The doctor continues to release the pressure on the cuff and listens until he or she hears no sound. That number (in this case 80) indicates the pressure in the system while the heart is relaxed (diastolic reading).
When the numbers are too high, that means the heart is working too hard because of restrictions in the pipes. Some hormones, like adrenaline (released when someone is under stress) cause certain blood vessels to constrict. This raises blood pressure. When people are under constant stress, their blood pressure goes up. This means their hearts have to work too hard. Blood pressure also can increase because of deposits in the pipes or because of a loss of elasticity as the blood vessels get older.
High blood pressure can cause the heart to fail (because it is working too hard). It can also cause kidney failure (from too much pressure).