We’ve said that there are 365 negative commandments, corresponding to the days in a solar year, and 248 positive commandments, corresponding to the limbs in a person. The days of a solar year are pretty easy to quantify (January 1, January 2, January 3, etc.), but what are the 248 limbs? How do we arrive at that figure?
The number of parts in the human body will no doubt vary based on whom you ask, for what purpose and using what criteria. A fifth-grader playing hangman will have far fewer than 248 limbs for his purposes and a med student may have many more. The context of this particular figure is from the Mishna in Oholos (1:8), regarding the parts of the human body that would convey ritual uncleanliness. (A whole limb conveys ritual impurity regardless of its size.) The Mishna lists 248 things that meet these criteria. It says:
There are 248 limbs in a person. 30 in the foot (six in each toe), 10 in the ankle, 2 in the shin, 5 in the knee, 1 in the thigh, 3 in the pelvis, 11 ribs, 30 in the hand (6 in each finger), 2 in the forearm, 2 in the elbow, 1 in the upper arm, and 4 in the shoulder. (This makes 101 on one side and 101 on the other.) 18 vertebrae in the spine, 9 in the head, 8 in the neck, 6 in the “opening to the heart” and 5 in the orifices. These transmit ritual impurity by touching, carrying, and under a canopy when they have sufficient flesh attached to them. Without sufficient flesh, they transmit impurity by touching and carrying, but not by a canopy.
It is understood by discerning people that a person’s body is not the actual person. The body is simply the "flesh" of the person, as is written "You have clothed me with skin and flesh, and covered me with bones and tendons"(Job 10:11)… the actual person is the (soul); the body is merely a garment the soul wears…
The same way that a tailor will make physical garment in the shape of a body, G-d similarly made the body, which is the garment of the soul, in the shape of a soul, with 248 limbs and 365 tendons ... (corresponding to) 248 spiritual limbs and 365 spiritual tendons… (so that) the 365 spiritual tendons of the soul “wear” the 365 physical tendons of the body …
…the food for the soul comes from fulfilling the Torah, which includes 613 mitzvos corresponding to the 613 spiritual parts. The Torah is called "bread" as is written, "Come, eat my bread" (Proverbs 9:5). Each of the 248 spiritual limbs gets its nourishment from a particular mitzvah that corresponds to that limb. When a person fails to perform that particular mitzvah, the corresponding limb will lack its proper nourishment…
• The Talmud in Nedarim says that the numerical value of Avraham – 248 – symbolizes the fact that G-d gave Avraham mastery over all his limbs.
• The Baal HaTurim on Numbers 5:18 points out that the word “ham’ar’rim” (“that bring a curse”) has a value of 496 – twice 248. That is because the bitter waters punish not only the body of the adulteress, but also her lover. (Two bodies = 2 x 248 = 496.)