This verse sets the scene for a pivotal moment in the history of the divided kingdom of Israel. Let's break it down:

"Behold, a man of God came out of Judah by Yahweh’s word to Beth El;" This introduces the main character: a prophet ("man of God") from Judah (the southern kingdom) who arrives in Beth El. The key is that he's there "by Yahweh's word." This highlights his divine authority and purpose. He's not acting on his own initiative, but on a direct command from God (Yahweh is the Hebrew name for God). Beth El is a significant location because Jeroboam (the king of the northern kingdom, Israel) has established it as a center of idolatrous worship.

"and Jeroboam was standing by the altar to burn incense." This introduces the opposing figure and the context. Jeroboam, the king of the northern kingdom, is personally overseeing and participating in the religious ceremony at the altar in Beth El. Burning incense was a common religious practice, but in this case, it's a sign of Jeroboam's establishment of illegitimate worship. The altar itself was likely dedicated to idols rather than Yahweh, or even if nominally to Yahweh, the worship was conducted in a way that violated God's commands.

In essence, this verse sets up a dramatic confrontation:

A divinely appointed prophet arrives at a place of idolatrous worship.
He arrives on God's authority.
He finds the king himself, Jeroboam, participating in the idolatry.

The verse foreshadows a confrontation between true worship and false worship, between God's word and human defiance. The prophet from Judah is about to deliver a message from God that challenges Jeroboam's actions and the entire system of worship he has established. This is the initial clash that will lead to a significant prophetic declaration against Jeroboam and the altar at Beth El (which happens in the subsequent verses).