The Torah in Chapter 15 describes the commandment of separating Challah from ones dough. In 15:20 and 15:21 it says from "the first of your dough".
The Torah uses the word "Reishit" a number of times. As far as I can remember, it is always in reference to one of the mitzvot hatluyot ba'aretz - a mitzva dependant on being in the land of Israel, generally one that has to do with agricultural aspects of being in Israel. Shemittah, Trumot and Maasrot, bikkurim, challah, etc..
The concept of giving from the first of ones produce or efforts is one of recognizing who is really the provider. The Jews wandered in the dessert for 40 years. They had all their needs taken care of and all their wants provided for. At worst they had to complain a little and then they were given what they wanted..
They are going to enter the Land of Israel and all that is going to end. Nothing will be given to them on a platter. They have to go back to living normal lives. They will have to work for their food. Plant, sow, plow, harvest - a lot of sweat and toil.
A person who works hard and eventually sees results from his labors, often takes the attitude that he has been successful in his efforts. We even say "Yagata U'Matzata, Ta'amin" - if you put forth effort and find success, believe (in your success). God tells us in advance that we should be careful from having such attitudes. When we give ourselves too much credit and forget who the actual provider is, we are headed for trouble. He therefore gave us a number of mitzvot whose goal is (or at leats in part) to protect us from having such thoughts and forgetting where our success really comes from.
After having planted and harvested and worked very hard for our produce, we are told to give the first fruits to the Kohanim and Leviim, or bring to the Bet Hamikdash, or let the land sit fallow for a year, or once a week stop working or separate from the first of the dough, etc. The first thing we do when we see the fruits of our labor is give some to Hashem (or His rep). This right away reminds us who really provided us with our success. It was not the toil of our hands and the sweat of oru brow. It was Hashem who made us successful. Don't forget it.