The Bible tells us in 1 Peter 2:5 that believers are "a holy priesthood" in a similar way that the Levitical priesthood was. The difference is, believers today are to offer "up spiritual sacrifices" not natural sacrifices as the Old Testament priests. However, like the Old Testament priests we are to minister to the LORD...
"And the Levites who went far from Me, when Israel went astray, who strayed away from Me after their idols, they shall bear their iniquity. Yet they shall be ministers in My sanctuary, as gatekeepers of the house and ministers of the house; they shall slay the burnt offering and the sacrifice for the people, and they shall stand before them to minister to them. Because they ministered to them before their idols and caused the house of Israel to fall into iniquity, therefore I have raised My hand in an oath against them," says the Lord GOD, "that they shall bear their iniquity. And they shall not come near Me to minister to Me as priest, nor come near any of My holy things, nor into the Most Holy Place; but they shall bear their shame and their abominations which they have committed. Nevertheless I will make them keep charge of the temple, for all its work, and for all that has to be done in it. But the priests, the Levites, the sons of Zadok, who kept charge of My sanctuary when the children of Israel went astray from Me, they shall come near Me to minister to Me; and they shall stand before Me to offer to Me the fat and the blood," says the Lord GOD. They shall enter My sanctuary, and they shall come near My table to minister to Me, and they shall keep My charge. (Ezekiel 44:10-16)
In the passage above Ezekiel describes two types of priests (Levites). One group (verses 10 & 11) was upholding religious practices, that is, ministers of the temple and to the people but not to God. Even though they made offerings to God, He didn't accept them, because they were not glorifying Him nor were they ministering to the LORD first and foremost from their heart. However, we see that the other group (verses 15 & 16) was ministering directly to the Lord, honoring Him as holy and obeying him with their hearts.
To "minister to the LORD" is to worship him alone in all that we do. Most often when believers think of worship it is limited to singing heartfelt songs to the LORD. However, Christian worship is any act of passionate devotion directed toward God that is motivated by an overwhelming feeling of profound love and admiration in all that believers do. So, any ministry that is directed towards others without first being directed towards God is not ministering to the LORD. This is why faith plays such an important part in a believers life. Hebrews 11:6 states, "But without faith it is impossible to please Him, for he who comes to God must believe that He is, and that He is a rewarder of those who diligently seek Him." This applies to every aspect of Christianity which includes "Ministering to the LORD".
At the Cross, Jesus became the ultimate sacrifice for all of humanity. He was both the sacrifice and the priest who presented the offering of Himself to God the Father. Hebrews 10:19-22 reveals that believers are covered by the blood of Christ and are now able to enter the "holy of holies" and present ourselves to God the Father. Ministering to the Lord does not mean that He needs us to stroke His ego; rather, it describes the kind of worship and service that God finds acceptable, that is, that which completely depends on the power of his Spirit, instead of flesh and blood. "But the hour is coming, and now is, when the true worshipers will worship the Father in spirit and truth; for the Father is seeking such to worship Him. God is Spirit and those who worship Him must worship in spirit and truth." (John 4:23-24)
As Christ was and is our example of both Offering and Priest, let us through faith in Him also offer up spiritual sacrifices as priests that are "Holy and acceptable to the LORD which is our reasonable service."