This verse describes a pivotal moment in the consolidation of David's power after the death of Saul and his son Jonathan. Let's break down the meaning:

"They brought the head of Ishbosheth to David to Hebron..."
Ishbosheth was Saul's son who had been ruling over the northern tribes of Israel after Saul's death. He was a rival to David, who had been anointed king over Judah.
Hebron was David's capital city at this time.
The act of bringing Ishbosheth's head is a brutal and symbolic act of demonstrating their victory and loyalty to David. It signifies the end of Ishbosheth's reign and, presumably, the end of the conflict.

"...and said to the king, “Behold, the head of Ishbosheth, the son of Saul, your enemy, who sought your life!..."
The men who killed Ishbosheth (Baana and Rechab, as mentioned earlier in the chapter) are presenting their "trophy" to David, emphasizing that they have eliminated his enemy.
The emphasis that Ishbosheth "sought your life" is crucial. It's meant to justify their actions and position them as loyal servants who have removed a threat to David.

"...Yahweh has avenged my lord the king today of Saul, and of his offspring.”"
This statement is deeply problematic for David. The killers are claiming that their act was divinely ordained – that God himself has avenged David against Saul's entire lineage.
The term "avenged" implies retribution or vengeance, not justice. This suggests that they see themselves as instruments of God's wrath against Saul's family.
By saying that God has avenged David against "his offspring," they are suggesting that all of Saul's descendants are legitimate targets.

In essence, this verse represents:

The brutal political realities of the time: Violence and assassination were common tools for consolidating power.
An attempt to gain favor with David: The killers hope to be rewarded for their actions by presenting it as an act of loyalty and divine favor.
A potentially dangerous situation for David: While the death of Ishbosheth removes a rival, it also comes with moral implications. David now faces the challenge of how to respond to this violent act that was committed in his name (or so they claim).

Why is this verse important?

It shows the complex moral dilemmas faced by David. He has to navigate political expediency with his own sense of justice and piety.
It reveals the ambition and ruthlessness of those around David. Not everyone is motivated by pure loyalty; many are seeking personal gain.
It foreshadows the challenges David will face in unifying Israel. The death of Ishbosheth, while seemingly advantageous, creates a moral quandary and raises questions about the means by which David's kingdom is being established.
It highlights the misuse of religious language for personal or political gain. They're using God's name to justify a heinous act.

David's response to this event (described later in the chapter) will be crucial in defining his character and the nature of his reign. As a righteous king, David rejects and punishes the murderers, even though they claim to have been acting on his behalf.