What does 1 Samuel 3:3 mean?

Joshua 18:1 describes how the tent of meeting between the Lord and His people was set up in Shiloh. Over time, it had likely become a semi-permanent tabernacle to the Lord. The ark of the covenant, upon which God's presence rested, may have been moved to Bethel for a time (Judges 20:26–28), but it was now in Shiloh.

Inside the tent of meeting, which is here called the temple of the Lord, was an area called the Most Holy Place or the Holy of Holies. This was where the ark of the covenant was kept behind a veil. Outside of that veil stood a lamp. The Lord had commanded that the lamp be kept lit from evening to morning by Aaron and the priests to follow him (Exodus 27:20–21; Leviticus 24:1–3). Samuel was lying down in that room, outside the Most Holy Place where the ark was kept. The boy (or young man) may have slept there regularly or may have been there to be available to help with various duties.

Since this verse says that the lamp of God had not yet gone out, it was likely near dawn when these events happened.