Blood flows slower in veins than arteries because veins have valves.
Veins carry deoxygenated blood back to the heart, whereas the heart pumps oxygenated blood through the arteries to the body. Because it is going to the whole body, this blood needs to be at a high speed and under lots of pressure. Thus the heart contracts and pumps it through thick, muscular arteries under high pressure.
Veins are thinner walled and have valves so that there is no backflow of deoxygenated blood due to the low pressure of the blood in veins. If veins were under high pressure they would gush into the heart and cause it to burst/explode.