Sniffing is a term used to describe eavesdropping on network communications.
Typically communications between one computer and another – particularly via the internet – travel across several different devices that are also shared with other devices and computers. Depending on how those devices are configured, it may be possible for a communication traveling across that device to be “seen” by other devices not actually involved in the conversation. The most common example is an open Wifi hotspot, where all wireless communications between computers and the hotspot itself can be seen by any other computer capable of wireless communication within its range.
The best analogy might be listening in on a conversation happening between two people near you.
Sniffing can be protected against in several ways, but the most reliable and common is to encrypt the conversation. The data might still be sniffed, but because it has been encrypted, it cannot be understood by anyone other than the parties actually involved in the conversation.
Think of it as those two people near you speaking in a foreign language, or a language known only to them – you can hear the conversation, but you have no idea whatsoever what’s being said.