When someone says to you, “here” or “now”, you probably know what he means. “Here” might the room that you are both sitting in. “Now” would be the span of time you spent sitting together. But if either word were uttered under different circumstances, it could mean something very different. For example, if I called you from the Andes and I used the word, “here”, it would mean a mountainside somewhere - possibly thousands of miles away from the aforementioned room. The same word can mean both the room and the mountainside because of deixis.
Deixis is a form of exophora, which is an utterance that is given meaning by the context it is uttered in. Specifically, deixis represents the speech event itself: deictic expressions reference the speaker, the speaker’s utterances, the speaker’s location, and the time at which the speech event occurs. There are different types of deictic expressions that refer to each particular aspect.
Personal pronouns, such as “I”, “you”, “he”, and “she”, are deictic expressions. “I” refers simply to the speaker. The other pronouns are defined by the relation the referenced person has to the speaker in the discourse. As the role of speaker switches from person to person, the context represented by deixis in understood by participants of the discourse to change too.
Location and time are a little more complicated. Whenever someone speaks - or writes, or is quoted, etc. - there is an implicit deictic center that is formed in the minds of the speaker and any listeners. A deictic center is the point in space and time that spatial and temporal deictic expressions refer to. “Here” and “now” are the simplest examples. The verbs “to come” and to “to go” are also spatial deictic expressions: “to come” means motion towards the deictic center, and “to go” means motion away.
Based on this analysis, the phrase “come here” seems redundant at first. But actually the addition of “here” can be important, due to a phenomenon called sympathetic deixis. It is not uncommon, especially in phone conversations, to hear an utterance like, “I will come by later”. For the speaker to move toward the deictic center is almost nonsensical when the speaker is the deictic center. But in this case sympathetic deixis causes the deictic center to shift from the speaker’s location to the listener’s location. So motion towards the deictic center actually translates to motion toward the listener.
Note that the shift caused by sympathetic deixis does not necessarily affect all the aspects of deixis. In the example above the meanings of personal pronouns do not change after the deictic center has shifted; in a similar sentence, “I will come to see you”, “I” refers to the speaker, and “you” refers to the listener - as would be expected with or without a shifted deictic center.
An especially fun deictic puzzle is often heard in answering machine messages like, “I’m not here right now”. It isn’t possible that the deictic center is fixed upon the speaker during this message, because it is not possible for the speaker to not occupy his own location. So there must be sympathetic deixis in effect to shift the deictic center either spatially or temporally. As someone who has been on the receiving end of this message, I expect “here” to mean the location where the message was recorded, and “now” to be the time when I am calling. By that analysis the spatial location of the deictic center remains fixed on the location of the speech event, while the temporal aspect shifts to the listening event via sympathetic deixis. There is another possible analysis where both spatial and temporal sympathetic deictic shifts occur. In that case the spatial shift does not move the location of the deictic center to the listener, but instead moves it to the place where the listener expects it to be: in this case wherever the speaker’s phone is. Under either analysis, the answering machine example demonstrates that deictic shifts can be temporal as well as spatial.
There are other forms of deictic expressions. There is a more complete list in the Wikipedia article on deixis.