Lactic Acid is a byproduct of anaerobic respiration during glycolysis (energy producing reaction cycle). ATP or Adenosine Tri Phosphate is formed, or energy. This energy is utilized in quick movements like getting up from rest or weight lifting. This energy is used until we go into aerobic respiration is utilized where oxygen is needed.

Lactic Acid builds up because over time glucose stores are depleted (source of energy), and we no longer have the carrier mechanisms to get rid of the built up lactic acid or to convert it back into glucose for more energy. As it builds up, many other toxins are being built up as well in our blood stream to toxic levels, and energy is no longer being produced at a fast enough rate to keep up with our energy consumption to exercise. The muscles don't have enough energy, become fatigued, and lactic acid remains.

Cooling down will allow your body which is constantly creating more ATP for energy to start building up its supply of energy again while circulating the blood more readily so the toxins can be diluted in your systemic blood. Moving the lactic acid around the body will decrease soreness. It is not solely lactic acid causing this soreness however, it is due to many other biological means as well. Cooling down will all your muscles to relax and get rid of built up toxins.

Lactic Acid.

http://sportsmedicine.about.com/cs/exercisephysiology/a/aa053101a.htm

From the above listed site:

While lactic acid may play a role in fatigue its supposed role in muscle soreness has been disproved and it is now being recognized as more of a positive player in metabolism. George A. Brooks has described lactic acid as a key substance used to provide energy, dispose of dietary carbohydrate, produce blood glucose and liver glycogen, and promote survival in stressful situations....

Although active recovery decreased lactic acid levels faster, it may also further deplete the glycogen stores that need replenishment. Therefore, a combination has been suggested whereby active and passive recovery are utilized together to decrease lactic acid levels while promoting maximal glycogen resynthesis. In other words, the athlete should warm down until normal rates of breathing return and then rest. At this time, a high carbohydrate meal should be consumed to help replace the glycogen stores, which have been depleted through exercise....

In summary, lactic acid is not a useless metabolic by-product. It can serve as a very important and useful energy source. However, if the lactate threshold is reached during exercise, excessive lactic acid can accumulate, causing fatigue. Fortunately, this negative effect can be partially offset by proper training, warm down, and a high carbohydrate diet.

LactiC acid is formed from pyruvate (a chemical formed from burning glucose for fuel during exercise), it builds up in muscles, not just the legs, during exercise when there is an absence of oxygen. When there is sufficient oxygen available to muscles lactic acid breaks down easily to carbon dioxide and water which are then removed by the lungs. "I feel the burn" - this is actually the sensation you feel when your body isn't getting enough oxygen to those muscles your working.

You need to cool down afterwards so your muscles don't cramp up quickly...have you ever used a pan when cooking and then put it in a sink of cool (not even cold) water? It contracts and releases steam. Ulimately, if you do this too much the pan won't be usuable anymore because it will crack...Same with the muscles in your legs (but they will tear)

Source(s):
I watched The Magic School Bus as a kid, they had a segment on it.
and
http://www.webmd.com/content/article/43/1676_53084

If the Magic School Bus is that informative, I'm going to have my kids watch it one day hahahaha! Thanks