This verse is spoken by Barzillai to King David after David has been restored to his throne following Absalom's rebellion. Let's break down the verse to understand its meaning:

"Your servant would but just go over the Jordan with the king." This is Barzillai expressing that he simply wanted to accompany David across the Jordan River, the point of re-entry into Israel, as a sign of respect and loyalty. He helped David by providing supplies and support while David was in exile. He feels he only did a small thing in his mind (a mere escort to the river).

"Why should the king repay me with such a reward?" David, in his gratitude, offered Barzillai a place at his court in Jerusalem, a high honor and privilege. Barzillai is saying that he doesn't deserve such a grand reward for what he considers a small act of kindness and loyalty.

In essence, the verse conveys:

Barzillai's humility: He doesn't see his actions as extraordinary and is surprised that David wants to reward him so lavishly.
His contentment: He's already lived a full life (he was quite old at this point) and doesn't desire the trappings of courtly life.
His loyalty: His motivation wasn't personal gain; it was genuine support for David as his rightful king.
A polite refusal: Barzillai is gently declining David's offer, implying that he's too old and settled to move to Jerusalem and participate in court life.

The verse highlights Barzillai's character as a selfless, loyal, and humble individual who values genuine connection over material reward. It also shows David's generous nature and his desire to acknowledge those who stood by him in difficult times.