I know what the cardiac cycle is. There are two phases diastole and systole. One is the relaxed, and the other is the contracted form of the heart. The diastole is where blood is pumped to the ventricles and systole is when blood goes to the aorta, and lungs. But what is the connection to blood pressure?
There are two levels to take your question at. The first is simpler but I'm not sure if it is what you are looking for:
If you imagine the heart and all the blood vessels in your body as a closed plumbing system with no leaks (not entirely accurate) then when the heart contracts and squeezes the blood from the ventricles the total surface area the blood is pushing against has decreased - there is more blood in a smaller space. This means that the pressure on the arteries from the blood has to increase when the heart contracts - in systole blood pressure is much higher than in diastole.
The second level is a little more in depth:
Cardiac output (a measure of how much blood is being pumped around the body to the organs where it is needed) is defined as the product of stroke volume and heart rate.
$$CO = SV \times HR$$
The relation of stroke volume to blood pressure is defined by Starling's Law. This states that the more blood that is in the heart, the more its walls are stretched. The more the walls are stretched, the harder the heart contracts in response. This increases blood pressure as again more blood is displaced from the heart.