When I think of when I have needed some patience this week, I'm thinking about how irritated I got when I was put on hold and had to listen to music I didn't like, or when there were lots of cars at the intersection when I wanted to be able to turn left immediately. But James is talking about a different situation that requires patience.
James is talking about our waiting, our anticipation, for the coming of the Lord. A farmer looks at the land where he's planted the crop. The crop's not showing yet. He's still waiting. But, as he waits, he is confident that rain will bring that crop up from the earth.
Beverly Gaventa, in Texts for Preaching, A Lectionary Commentary based on the NRSV-Year A expresses it this way:
Like the farmer who relies on God to send the needed rain (Deut. 11:14; Jer. 5:24; Zech 10:1), the faithful may and must rely on God. Patience derives from that certainty about God's protection.