The lower limb is a technical name of what is commonly known as the "leg". Anatomists and doctors are very particular in naming structures in the body, thus they often having slightly different terms for common parts of the body. The leg has a complex structure and is very important for a person to be able to get around. Of course, all of the muscles in the leg require blood to function. The structure and route of the arteries of the lower limb is somewhat complicated, but understandable.
All blood begins its journey through the body in the heart. Blood leaves the heart through the aorta, which is the largest of the arteries. As the aorta travels, it gives off branches that lead to all of the muscles and organs in the body. The aorta quickly turns downward, travelling through the abdomen. Around the level of your belly button, it branches in to arteries called the right and left illiac arteries.
The illiac arteries then immediately split (before they reach the leg) in to the internal and external illiac arteries. Remember, this is happening on both sides of the body - there are to of each artery being described (except the aorta).
The external illiac arteries travel through the pelvis, eventually becoming the femoral arteries. The femoral artery is the major artery that supplies blood to the entire leg. It runs on the inside (medial aspect) of your thigh.
Part way down the thigh, the femoral artery begins to move toward the back of the thigh. Along the way, it is giving off numerous smaller branches, all of which supply blood to parts of the thigh. Some of these branches have names, such as the superficial illiac circumflex, deep femoral, superficial external pudendal, and the superficial epigastric arteries - among others. It's a real nightmare of confusion for anatomy students.
About at the level of the knee, the femoral artery officially becomes the popliteal artery. From here, things get really crazy. The popliteal artery has a TON of important branches, each of which being responsible for supplying blood to various parts of the lower leg.
Let's name a few of the important branches of the popliteal artery. There are the anterior and posterior tibial arteries. These are mostly involved in supplying blood to the front and back of the lower leg. They each give off numerous named branches themselves. These are certainly two of the more important branches of the popliteal artery.
Then there the medial and lateral superior genicular arteries. There is also a middle genicular artery. And don't forget the sural artery - of which there are actually up to a half dozen in some people. They supply the calf muscles.
Oh, and before you think your off the hook, don't forget the medial and lateral inferior genicular arteries. Whenever you seen a "superior" artery, you can be sure there is a corresponding "inferior" in there somewhere. If you're confused yet, don't worry, you're not alone.
There a couple of places where the arteries of the lower limb can be felt, along with the pulse. The femoral artery can be felt in the inner thigh on most people. The popliteal artery can be felt in the back of the knee much of the time.
The structure and route of the arteries in the lower limb is confusing, especially without the aid of pictures. Hopefully, this gave you something of an introduction to the anatomy of these arteries.