Nearby Month
  
You are diffusing a bomb. You don't really know what you're doing, but you're on the phone with the bomb squad and they are walking you through the process. You ask, "what wire should I cut?" They respond, "the nearby wire." First, you might wonder whether English was their first language. But leaving the weird syntax aside, which wire would you cut?
Right...the one closest to you. The nearby wire.
Same logic applies to the term "nearby month." It's the month closest to us now. The one nearest in the future. The term comes up in derivatives trading, when you need to know which month has the closest expiration date.
Derivatives trading (like options or futures) involves contracts that have different expiration dates. You can buy an option that expires next month, or in two months, or three months, or...well, we assume you know how to count. You get the idea.
The nearby month is the most recent expiration for a derivatives contract...the most recent contract you can buy.