One of the goals of this site is to translate the Greek words of Christ as the people of Christ's time would have heard them. Many Greek words are translated somewhat inaccurately in most versions of the Bible. This problem starts with the Greek word translated as "word" in the Gospels. Since this site is about Jesus's "words," we should start there.
The correct Greek word for "word" in English is lexis. Jesus is never quoted as using the Greek word, lexis, in the NT. In the Bible, the most common Greek word translated into English as "word" is logos, not lexis. Logos means "computation", "relation", "explanation", "law", "rule of conduct", "continuous statement", and so on. The English words that come closest to capturing all the meaning of logos are "explanation", "idea", "concept", or "logic". Logos is the source of our English word "logic." It is also the root word for all the English words that end in "-ology," which we use to mean "the study of" something. The people listening to Jesus speak when He spoke in Greek would not have heard Him say "logos" and thought "He meant to say lexis".
Words That Don't Mean "Word"
Logos is not the only word in the Bible translated as "word" thougb it is by far the most common word translated into "word." In Mat 4:4 a different Greek word is used. (click on the link to see another article written on the Greek of this verse). Christ is quoted as saying "Man shall not live by bread alone, but by every word that proceeds out of the mouth of God." Here the Greek word is rhema, which means "that which is spoken", "saying", "subject of speech", and so on. The English word "remarks" is from the same base and captures the main sense of rhema idea well. This Greek word, however, does come close to the idea in English that logos means because rhema refers only to what is spoken, closer to our word "remarks," which is descended from it.
However, looking a little more deeply at Mat 4:4, the quote is from the old testament, Deu 8:3, where the Hebrew word translated into rhema in the Septuagint (the Greek OT) is mowtsa'. Mowtsa' doesn't mean "word" in English either. It may be even further from "word." This Hebrew word means a "going forth", "rising (of the sun)", "going forth of a command", "that which goes forth," and a "place of going forth." The "going forth of a command" comes closest to the idea of "word," especially in the context of a "mouth." However, what goes forth from God's "mouth" might also be described, at least by Jesus, as "breath," which is the Greek word for "spirit" (see this article on the meaning of "spirit").
So What Did Jesus Mean?
While our English word "remarks" comes very close to the same meaning as rhema, the problem is logos, which is used much more frequently. The English word most directly descended from it, "logic," doesn't really work. That word has become too closely associated with reasoning, especially formal reasoning.
The common meaning of logos in Greek as "explanation," works well in most contexts in which Jesus uses it. However, in a few verses, specifically Mat 12:36, Mat 18:23 and Mat 25:19, Jesus clearly uses it in the sense of more in the sense of "accounting" since the context is numerical amounts, but "explanation" still works. Its meaning as "discussion," doesn't work, because most of what Christ uses as "word" to refer to is not a "discussion" in the sense that there are two sides. (If you look at the quotes with "word" in them, on the right side of them you will see that Jesus used the word logos in a way that clearly meant what he was explaining, or, more precisely, what he was given by the Father to explain, not general topics of this discussion.)
We also have to deal with the fact that logos is used in both in the singular, explanation, and plural, explanations. In the singular, Jesus seems to use it to refer generally to all he has said, that is, "the explanation" that he has offered. The only problem with "explanation" is that it is a long, somewhat cumbersome word.
In English, we have a couple of other options that are not typically used in NT translation. The word "teaching" and especially the word, "lessons," both work well. Both capture the basic idea of the logos as an "explanation," that is, the logic of something. The word "lessons" seems to fit well in the modern vernacular because it is used more generally that "teachings." While teachings come from a teacher, lessons come from life, mistakes, and God as well as a teacher. Jesus uses logos in all of these ways.
However, the words "lessons" and "teachings" are very education oriented, at least as we use them today. In Jesus's time, people didn't go to school for the first part of their life, as we do now. Life's lessons were learned by living and listening to people and, for the Jews, discussing the scripture. Today, we more commonly use the terms "ideas" and "concepts" to refer to logical (logos) explanations for things. Because "ideas" also has the sense of new inventions in English, perhaps our words of "concept" and "concepts" comes the closest to the concept Jesus was trying to express when he used the term logos. How, "concept" is a little sterile and academic. Currently, I think I prefer "ideas" because it is shorter and pithier.
So, we could call this site "Jesus's Ideas" except that this site really is about "words" in the sense of lexis, not just logos. In either case, "The Word of God" is much larger than any one word can represent. So, perhaps we should not translate some words at all, and just say "The Logos of God".