The Literal Commandment
Command Aaron and his sons, saying, 'This is the law for the burnt offering: the burnt offering itself shall remain on the hearth on the altar all night until the morning, and the fire on the altar is to be kept burning on it. (Leviticus 6:9)
The literal commandment is to keep the fire that is on the altar burning.
Messiah Says
Messiah implicitly affirmed this commandment when He spoke about the Law:
"Do not think that I came to abolish the Law or the Prophets; I did not come to abolish but to fulfill. For truly I say to you, until heaven and earth pass away, not the smallest letter or stroke shall pass from the Law until all is accomplished. Whoever then annuls one of the least of these commandments, and teaches others to do the same, shall be called least in the kingdom of heaven; but whoever keeps and teaches them, he shall be called great in the kingdom of heaven. (Matthew 5:17-19)
Pictures of Messiah
Messiah declared that He came to cast fire upon the earth, "and how I wish it were already kindled!" (Luke 12:49)
Perhaps in this commandment regarding the continual fire of the altar we can find Messiah and the fire that He wished to kindle.
The fire was to ignite and consume the offering on the bronze altar in the Temple.
The Holy Spirit appeared as tongues of fire on the believers during Pentecost (Acts 2:3) which caused those who received Him to burn with a passion such that their bodies became "living sacrifices". (Romans 12:1)
Just as the earthly priests continually kept the physical fire burning on the altar so, too, our Great High Priest continually keeps the fire of His Spirit burning in our hearts and minds.
How Messiah Fulfilled
Messiah fulfilled this commandment by not participating in it. The commandment is given to the Levites as part of their service. Since Messiah was not of the tribe of Levi He did not bear responsibility to perform this commandment.
Traditional Observance
The traditional observance of this commandment was the literal fulfillment by the Levites to keep fire continually burning upon the altar.
It seems obvious that fire was necessary to burn the sacrifices which were to be offered continually so why this explicit commandment to burn fire upon the altar? It was interpreted to mean that G-d had given a separate commandment to have a separate fire burning upon the altar that was not used for burning the sacrifices. This, along with another commandment, led to the tradition of burning three fires on the altar
Other Notes
Absent the Temple, a functioning Levitical priesthood, and the bronze altar we are unable to literally fulfill this commandment today.
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