The sacrificial offerings of Leviticus are not insignificant, primitive, or barbaric. God carefully devised them as teaching tools to those under the Old Covenant, who looked forward to the full revelation of the object of His law, and to those of us under the New Covenant, who look back on it.
There are five different kinds of offerings given within the first 6 chapters of Leviticus. Beyond this the first seventeen chapters of Leviticus are devoted to explaining the occasions for, and the correct procedures to be followed in, sacrifice. It is clear then that Sacrifice is important to Leviticus’ presentation of Israel’s worship.

We will look at the five types of worship and summaries for each of them, why they play an important part.

The burnt sacrifice shown in Leviticus one is the most important of all the sacrifices offered to God. This is mainly because it expressed dedication. This sacrifice, unlike any other, was wholly consumed and is also described as the whole burnt offering. Offerings would be graded in value so that even the poorest worshippers might find access to God by coming in complete devotion. 

The sacrifices signified that the whole of man, for whom the sacrifice was offered, was to be entirely offered or devoted to God's service.
It is amusing that the meat offering in Leviticus 2 was the one offering that did not consist of meat. The proper translation is “meal offering,” which would be an offering of grain or cereals made of fine flour. The word translated ‘meat’ in Hebrew simply means a present. The primary idea behind this this offering is that it is a gift presented to God as an act of worship. Yet, because this offering was the product of the soil and the result of man's labor, it symbolized the consecration of the results of worship to God. The ingredients included are also hugely significant. The oil has been recognized as a symbol of the Holy Spirit (1 Samuel 16:13, Isaiah 61:1, Luke 4:18). People who are dedicated to God can expect the power of His Spirit to guide, aid, and empower them on a daily basis. Frankincense was incense of high quality it symbolized prayer and praise. The reference to salt indicates that the act of sacrifice was a reminder of the eternal covenant relationship between the worshipper and his God.
The peace offering in Leviticus 3 had at its core, the concept of fellowship. This concept was laid on the altar and burned as a gift to the Lord, part was given to the priests, and the worshipper ate the remainder. It expressed joy, peace, and gratitude, but also sharing, joint participation, fellowship, and friendship. Such are the characteristics of true worship.
The sin offering in Leviticus 4 was required of all; priests (verses 3-12), the congregation as a whole (verses 13-21), rulers (verses 22-26), and common people (verses 27-35). It made atonement for sins done through ignorance. Either the perpetrator would have known the law but unintentionally violated it, or he acted without knowing he has done wrong. The justice of God was shown, in that degrees of guilt were thus recognized. Not all sins were equally heinous. The sin offerings were of different kinds, according to the rank and responsibility of the offender. This indicated that there were degrees of responsibility corresponding with the rank and position of the people concerned. The sin of a ruler, because of his wide influence, might create a greater scandal and bring more reproach on the name of God than the sin of a lone man.
The Final offering in Leviticus 5 and 6 may be termed the guilt offering, and it symbolized satisfaction or restitution. It should be regarded as a particular kind of offering for a particular kind of Sin. It related to invading or disregarding the property of another person. In every case and for all people, the offering was in the form of a ram. This was different to a sin offering, which had gradations of offering based on the Sin. 
 The spiritual meaning is that everything on this earth belongs to God, but is entrusted to man as a steward.

Sacrifice, ultimately, is an offering of something valuable, as a sign of an interior offering of ones-self. An expiatory offering is a sign that one's own sins are placed humbly into the fire of God, and then annihilated by his mercy. Jews over the centuries came to understand that the actions they performed were really about themselves in relation to God, not about something external to themselves; it was not that God needed animal victims, but rather that they needed to express our praise, thanksgiving, penance, etc., by means of visible signs. We know from the Gospels that this legislation runs the danger of hardening into legalism, but without the law there would never have been a receptive dwelling for Jesus Christ in the bosom of the human race. Leviticus has a much greater purpose than first suggested on reading. This purpose was to prepare Israel for the one who truly redeems through an eternal sacrifice, and saves mankind, namely, Jesus Christ.

Word Count 935

Bibliography

Harrison, R.K. 2008 Leviticus: An introduction and Survey 1st Ed. Inter Varsity Press

Mackintosh, C.H 1880 Notes on the Book of Leviticus Kindle Edition, Amazon

Watts, J. W. 2007 Ritual and Rhetoric in Leviticus: From Sacrifice to Scripture 1st Ed. Cambridge University Press

Tidball, D. 2005 The Message of Leviticus 1st Ed. Inter Varsity Press