This verse is part of the Parable of the Unmerciful Servant, found in Matthew 18:21-35. Here's a breakdown of what it means within the context of the parable:

"So his fellow servant fell down at his feet...": This mirrors the initial action of the first servant, who owed a massive, unpayable debt to the king. He's mirroring the same posture of desperation and humility.

"...and begged him...": The fellow servant is pleading for mercy. He recognizes his debt and inability to pay it immediately.

"...saying, ‘Have patience with me, and I will repay you!’": This is the key. The fellow servant acknowledges his debt and makes a promise to repay it. He's not asking for forgiveness, just for patience and time. He believes he can, given enough time, repay what he owes.

In essence, this verse illustrates:

The commonness of debt and obligation: People often owe things to each other, whether financial or otherwise.
The plea for understanding and leniency: People in debt often ask for more time or easier terms of repayment.
The possibility of repayment: The servant believes he can, with time, fulfill his obligation.

Within the larger parable, this verse serves to highlight the contrast between the king's (God's) mercy and the first servant's (our) lack of mercy. The first servant, who had been completely forgiven an enormous debt, is unwilling to show even a small measure of patience to someone who owes him a much smaller amount. This stark contrast is the point of the parable – to show the importance of forgiving others as we have been forgiven by God.

So, the meaning of the verse is not just about financial debt. It extends to:

Forgiveness: The need to forgive others as we have been forgiven.
Mercy: Showing compassion and understanding to those who are in need or have wronged us.
Grace: Extending undeserved favor to others.

The parable challenges us to examine our own hearts and ask whether we are truly living out the forgiveness and mercy we have received from God.