Separating Challah-Hafrashat Challah

(30) And the first of all the first-fruits of every thing, and every heave-offering of every thing, of all your offerings, shall be for the priests; you shall also give to the priest the first of your dough, to cause a blessing to rest on your house.

(6) Women die in childbirth for three transgressions: If they are not careful with [the laws] of menstruation; and if they are not careful [to separate some] Challah [when baking]; and if they are not careful with the lighting of the [Shabbat] lamp.

I have called you the first (Jer. 2:3 "Israel was holy to the Lord, the first fruit of his harvest") therefore I have cautioned you concerning matters of the first (of the dough, i.e. Challah tithes). The soul that I have placed within you is called a candle thus I have cautioned you concerning matters of candles ( kindling the sabbath lights). If you fulfill these responsibilities all is well; but if you do not I will take back your souls.

(18) Speak to the children of Israel, and say to them: When you come into the land where I bring you, (19) then it shall be that when you eat of the bread of the land, you shall set apart a portion for a gift to the LORD. (20) Of the first of your dough you shall set apart a cake (Challah) for a gift; like that which is set apart of the threshing-floor, so shall you set it apart. (21) Of the first of your dough you shall give unto the LORD a portion for a gift throughout your generations.

Regarding Challah and lighting Shabbat candles-Because these are among the needs of a household, and she is found at home, and therefore she is bound to them.

Adam was the "Challah" of the world as the verse says "God created Adam from the dust of the Earth". When a woman mixes the flour with water she must take Challah to atone for the transgression of Chavah who caused the fall of Adam.

Rabbi Hunna said in the name of Rabbi Matanah: The world was created in the merit of three things--challah, tithes, and first fruits. The verse "In the beginning God created" refers to challah, as it says (Numbers 15:20): "The beginning of your doughs." It also refers to tithes, as it says (Deuteronomy 18:4): "The beginning of your grains." It also refers to first fruits, as it says (Exodus 23:19): "The beginning of the fruits of the land."

(2) From the root of the commandment - since the life of a person is dependent on food, and most of the world subsists on bread, Hashem desired to give us merit with a constant commandment in our bread, so that blessing should be placed in it through the commandment, and through it, we will accept merit in our souls. It turns out that the dough is food for our body and food for our soul. Additionally, so that the servants of Hashem, those that constantly strive in His work - and these are the Kohanim - should live without any toil at all. Whereas by the Terumah of the silo there is work for them, to pass the grain through the sieve and to grind it, here, their food will come to them without any pain whatsoever.

(17) Rabbi Elazar ben Azariah says: If there is no Torah, there is no worldly occupation; if there is no worldly occupation, there is no Torah. If there is no wisdom, there is no fear; if there is no fear, there is no wisdom. If there is no understanding, there is no knowledge; if there is no knowledge, there is no understanding. If there is no flour, there is no Torah; if there is no Torah, there is no flour.