In the KJV and most other translations of the NT, the Greek word translated as "come" doesn't have the same narrow meaning as the English "come". However, despite its different shades of meaning, most Biblical translations stick to the "come" translation even when they have to add ideas to make that sense work. Christ often uses this Greek word to mean "come" as well, but not always.
The actual Greek word is erchomai, which primarily means "to start," and "to set out." However, it usually has more the sense of "set out" because it usually refers to starting some form of motion. It doesn't mean "start" in the sense simple of beginning something, at least, Christ doesn't use it that way. This is why it can be used to mean "to come" and "to go." It means "to go" on a journey, that is, "to start a journey." However, it also means "to arrive" at a place." In English, we don't usually talk about an arrival as "starting someplace," except in the sense of starting in a workplace, but in Greek, that concept works fine.
Movement without Direction
What the word erchomai, does not imply is the concept of moving toward something, as our word "come" does. If the speaker wants to describe movement toward something with this word, he uses a proposition that means "towards" or he uses a variation of the word where the preposition is included as part of it.
Because of this, there are a number of Greek words, all of which Christ commonly uses, where erchomai includes a prefix indicating direction. "Go away" is from aperchomai. "Go in" is from eiserchomai. "Go out" is from exerchomai. "Go by" is from parerchomai. Though the "go" examples are used above because they are the most general, these words can also be translated with "come," as "come away", "come in", "come out," and "come by" or with "start", as "start away", "start in", "start out", and "start by".
In English, however, "come" has the sense of moving toward the speaker, while "go" often has the sense of moving away from the speaker. We do have ways of describing movement in English that are more vague in terms of direction. These capture the sense of this Greek word in ways the neither "come" or "go" do. The English phrases of "being under way," for example, communicates the idea that someone is moving without implying a direction.
The Beginning of the Journey
Neither "go" or "come" implies the sense of starting the movement the Greek word translated as "come" does. In English, we would use the phrases "he is starting out" or "he is setting out" to describe movement in this way. However, in English, we need the adverb "out" to give "start" its sense of motion Note that both of these phrase lack any implication of moving toward or away something. However, the sense of beginning is perhaps stronger than in the Greek word, at least how Christ uses it.
In some uses, this Greek word has a very strict sense of starting something. Our word "enter" has a bit of this feeling. For example, when we start a court case, we say that we "enter a charge." "Enter," in English, as with the Greek erchomai, has a sense of something beginning that is inherent, but it still primarily implies a type of motion. "Enter," however, has a more limited sense of movement than the Greek word does.
An Illustrative Verse
The word erchomai sense of starting something is important in understanding many of Christ's statements, especially in seeing the wordplay in them. The example we will use is John 12:46, which the KJV translates as "I am come a light into the world, that whosoever believeth on me should not abide in darkness." Most others translate this phrase as, "I have come as a light in the world." However, in the Greek source, there is no word that can be translated as "as." The KJV is more accurate because it doesn't insert the "as," but it looks odd because of the "am come" phrase, which we don't see in modern English. The verb form "am come" seems to be the present tense but the tense of the Greek verb is of an action completed in the past, so "have come" is better.
The Greek is clear. The direct translation of the Greek is "I have started a light in the world." This translation is certainly consistent with Christ's message. The verb is in the form that takes an object. The word for "light" is in a form that makes it the object of the active verb. It is in a tense that indicates that the action was is completed in the past. Al of these facts create problems for translators who prefer to always use the "come" translation." A more accurate version would be "I, a light, have set out in the world."
But in Greek, there is still more. The idea of "starting a light" is hidden in the verb. Interestingly, the form of the word for "light" could make it the object of the verb. So, Christ could have been saying directly "I have start a light in the world" at the same time as saying "I, a light, have come into the world." This makes the statement much more clever and interesting.
Why the Complete Meaning is Important
This real meaning of"come" is very important to much of Christ's message and it is lost by simply translating erchomai as "come." Almost every time Christ uses this word, we can discuss his statement in terms of something being under way at its beginning. However, it is often misleading to think that whatever is underway is coming toward us.
For example, in the Lord's Prayer (discussed in an early article here), Christ says, (as usually translated) "Your kingdom come." From this analysis, we can think of this more accurately as meaning, "Your kingdom is getting under way." God's kingdom is moving but it isn't moving toward us or away. And, in some sense, certainly in Christ's time and perhaps even now, it is just getting started.
Why is this more accurate sense of the word usually ignored in most translations? Possibly because we want to think that the kingdom is coming to us, like a bus on a route. And we want to think it is arriving soon, not that it is just starting out.