“the priests, the Levites.” Every priest was from the tribe of Levi, but the priests were descendants of Aaron, the brother of Moses, who were from the tribe of Levi.
“the ark of the covenant of Yahweh.” The ark represented the very presence of Yahweh Himself, and as such is mentioned ten times in Joshua 3 alone (Josh. 3:3, 6 (2x), Josh. 3:8, 11, 13, 14, 15 (2x), and Josh. 3:17). And the fact that the ark is in the Jordan while Israel crosses over into the Promised Land showed Israel that it was Yahweh Himself who was holding back the water of the Jordan River, and so it was “Yahweh of Armies” that was fighting for Israel even as they enter the Promised Land. The fact that the ark of the covenant went first into the Jordan is a picture of the God of Israel leading His people to victory. The name, “the ark of the covenant of Yahweh” occurs five times in Joshua (some 30 times in the Bible) and is one of several names that describe the ark. For example, it is called “the ark of the testimony” a number of times, including Joshua 4:16, and nine times in Joshua it is simply called the “ark of Yahweh” (Josh. 3:13; 4:5, 11; etc.). The name here in Joshua 3:3, “the ark of the covenant of Yahweh your God” may emphasize the king-vassal covenant in which Yahweh, the people’s God, is leading His people to victory in battle.
“and the priests, the Levites, carrying it.” In the wilderness wanderings, God put a pillar of cloud over the Tabernacle by day and a pillar of fire by night (Exod. 40:38), and when the cloud over the Tabernacle moved, the children of Israel moved and followed it (Exod. 40:34-38). The Bible never mentions when the pillar of cloud and fire disappeared, but it had by this time and the people were now to follow the priests carrying the ark, not the pillar of cloud. In fact, the 2,000 cubit distance between the priests and the rest of the Israelites was so that the Israelites could tell where the priests were going and then follow them (Josh. 3:4).