Closeness

There are so many types of korbanot (sacrifices or offerings; it is a word that cannot be accurately translated along with its nuances). Some are private, and some are communal. Some are for sins, and some are to celebrate holidays. Some are to offer personal thanks, and some deal with complex personal situations of a variety of types (sota, metzora, nazir).
Rav Shimshon Raphael Hirsch points out that korbanot are described as brought for and before Hashem (the main Name, Yud-Keh-Vuv-Keh). The Name of Elokim is never used in this context. As we know, the former represents the more merciful side of Hashem, whereas the latter represents His side of din (strict judgment). He explains that Hashem did not introduce the korbanot to demand that which is coming to Him but to present an opportunity. A person brings forth an object that relates to him and presents it toward Hashem in a manner that represents the person’s desire to himself draw closer to Him.
The first of the korbanot presented in Sefer Vayikra, where the personal korbanot are listed and the rules and categories are taught, is described as follows: "Should a person bring forth from amongst you a korban to Hashem" (Vayikra 1:2). It is appropriate and telling that this is referring to a korban nedava (voluntary) (Rashi, based on Torat Kohanim ad loc.). After all, the whole concept starts with the desire that one draw close to Hashem, and this is accomplished best when one does so in a voluntary manner.
The Torah continues (ibid. 3): "To the opening of the Tent of Meeting shall he bring it forth, according to his will." On the one hand, the Torah seems to cling to the idea of volunteerism and personal desire. However, the gemara (Arachin 21a) says that it is actually referring to forcing the person to bring the korban that he accepted. In order to be able to reconcile coercion with "his will," the gemara explains that we force him until he declares that it is his will. The gemara (Bava Batra 48a, although the idea is usually quoted from the Rambam, who expounds slightly) explains that a person wants to do the right thing and the coercion helps him combat those elements that are keeping him away from doing so.
The picture we receive of this entire korban process is the following. The point of the korban is for it to be an expression of one’s desire for closeness to Hashem. As such, there is little point of doing it as a technical act that does not capture a person’s sincerity. Nevertheless, while such a matter can start as one’s own voluntary idea, it cannot remain voluntary forever. Once he becomes obligated, it is enforceable. Yet, the desire to go through with the korban is a basic truth that relates to a person’s inner nature, which we can assume yearns to cling to Hashem (Tehillim 42:3). One needs to know that when he makes the promise to bring a korban, it will be done according to the strict rules that apply and that his promise will not be dismissed easily.