The oil that burns in our oil-lamps, "“τον του Θεού υπεµφαίνει έλαιον”" writes St. Symeon of Thessaloniki, the mercy
of God that was revealed when the dove returned to Noah's Ark to signify the
cessation of the flood, having in the beak an olive branch, or when Jesus,
prayed at length, He watered with the sweat of His clots the olive tree, under
the branches of which He knelt on the dreadful night on the Mount of Olives. Of
course, we all know how infinitely superior of the material light is the
internal light, a light lit by the Holy Spirit. So wrote the God-bearer Father
Gregory Nazianzus: “Φωτίσωµεν… γλώσσαν” “Let us lit…the tongue” and the commentator adds:
was this achieved? The oil symbolizes the infinite mercy of God, but the
oil-lamps also, symbolize the Church that is imparting of the Divine Mercy and
lighting. They also symbolize the saints themselves that their light shone
according to the word of the Lord, "let your light shine before others,
that they may see your good deeds and glorify your Father in heaven." (Mt.
5:16)
There are many reasons for which the Orthodox we should lit the oil-lamp,
for example:
1.In order to remind us of the need for prayer.
2. To illuminate
the space and to drive-away the darkness where the evil forces are dominant.
3. To remind us that Christ is the only true light and the faith in Him is
light,
4. To remind us that our lives should be bright.
5. In order to remind us
that as the candle requires our own hand to light thus the soul requires the
hand of God, that is His Grace.
6. To remind us that our will must be burnt and
be sacrificed.
7. For the love of God, and many more...
Needless to say, that the
vigil-oil should be an olive oil and the best possible quality. Besides, the
Lord prayed in the garden of Olives and the temple with the oil-lamps is
converted to a new garden and mercy (oil) and Divine Mercy, their oil reminds
us of the compassion of God and their light in our lives, that should be bright
and holy. The shedding of light in the temple symbolizes the divine light of
God's presence that illuminates the hearts not only of neophytes but all
Christians as well. The Lord revealed this great truth about Himself in the
following words: "I am the light of world"(John 8:12). He is light
not only because of His luminous teachings, but mainly due to His luminous
presence. This is confirmed by the particular miraculous Transfiguration, where
"His face did shine as the sun, and His raiment was white as the
light."(Matth.17:2).

Source: http://orthodoxinfo.com/general/The-Meaning-and-Use-of-Candles-Incense-and-Vigil-Lamps.pdf
CONVERSATION