According to the venerable Strong's Concordance (#G4487), Rhema means an utterance (individually, collectively or specifically) on a particular matter or topic. Thayer's Greek Definitions defines the word as something that has been uttered, in either the past or the present, by a living entity.
The first time Rhema is used in the New Testament is during Jesus' forty-day temptation by Satan. Jesus, after being tempted to feed himself through a miracle after fasting for a long period, responds with the following.
But He (Jesus) answered and said, "It is written, 'Man shall not live by bread alone, but by every word (Rhema) that proceeds out of the mouth of God.'" (Matthew 4:4, HBFV)
Interestingly, the word Rhema occurs at least seventy times in the New Testament Greek text. The books that use it the most are the gospel of Luke (19 times), followed by the book of Acts (14 times), then the gospel of John (12 times). In the King James Bible, the Greek word Rhema is many times translated as "word(s)" (Matthew 4:4, 18:16, Mark 14:72, etc.). It is also translated as "saying(s)" (Mark 9:32, Luke 1:65, etc.) and "thing" (Luke 2:15, Acts 5:32).
The word's second appearance in the New Testament occurs in Matthew 12 when some self-righteous religious leaders accuse the Lord of casting out demons by the power of Satan himself. He warns them that God will hold humans accountable for every idle (lazy, useless) word (Rhema) that is spoken (see Matthew 12:24, 36).
In the Greek language, the word Logos (Strong's Concordance #G3056) can also be translated as "word" in a number of English translations, such as in John 1:1, 14, Luke 1:2 and many other places.
Some Pentecostal Christians view Rhema as the Holy Spirit's 'voice' that guides a believer or that offers a person some kind of special revelation that is not clearly revealed in Scripture. Many Charismatic teachers promote the belief that there is a distinct difference between the meaning of this word and Logos, even though both are translated the same in most Bibles. Most Greek scholars, however, state that the New Testament writers made no such clear distinction between these two terms in their writings.