The standard structure of the shacharit and mincha service is for the congregation to first recite the shemoneh esrei quietly, followed by the chazzan who then repeats it out loud. There are two reasons why the sages instituted a public repetition of the shemoneh esrei. It seems that the primary purpose for this enactment was for the benefit of those who did not know how to read or pray. Such individuals were permitted to discharge their obligation to pray by merely listening attentively to the public repetition of the shemoneh esrei and answering "amen" at the conclusion of the blessings. The other more prominent function that the repetition serves is in order to allow the congregation to recite the kedusha.
Nevertheless, when time is running short or the members of the minyan are unable to remain assembled for a prolonged period of time, many congregations implement an abridged form of the repetition, known as the "heicha kedusha". When the heicha kedusha form of repetition is used it is generally only the first three blessings of the shemoneh esrei which are recited out loud. This abbreviated form of the repetition is generally only used at mincha time, but is occasionally employed when needed at shacharit, as well.
There are a number of customs on how the heicha kedusha repetition is performed. Some authorities recommend that everyone begin reciting the shemoneh esrei together out loud when performing a heicha kedusha saying it word for word with the chazzan, including the kedusha. Common Ashkenazi custom, however, is for the chazzan to begin the shemoneh esrei out loud alone while the congregation responds to his blessings and recites the kedusha responsively, as if it were a regular repetition. According to all customs, at the conclusion of the kedusha the chazzan continues silently to himself while everyone else then begins their own silent shemoneh esrei from the beginning.
There are a number of other methods for performing the heicha kedusha, as well. In situations where time is very short, however, such as at mincha when there are only one or two minutes remaining before sunset, it is best that everyone commence their shemoneh esrei at the same time as the leader. Incidentally, in the event that when one is about to begin the silent shemoneh esrei one notices that the chazzan is about to begin his repetition, one should recite the shemoneh esrei along with him word for word – at least for the first three blessings.
Among the rationalizations for doing a heicha kedusha and forgoing the full repetition is because, as mentioned above, the primary purpose of the repetition was for the benefit of those who did not know how to pray on their own. In fact, those who are able to pray on their own, as is the case with most people today, are forbidden to rely on the repetition to discharge their obligation to pray. Therefore, since most people are able to recite the silent shemoneh esrei on their own, either in English or Hebrew, the need for a repetition in our day is minimized. Indeed, it is reported that the Rambam did away with the repetition of shemoneh esrei entirely because people weren’t properly paying attention to it or responding "amen" when required.
Make no mistake, the repetition of the shemoneh esrei is one of the enduring enactments of our sages and must never be compromised. Indeed, there was once a "cherem" placed on congregations that did not conduct the repetition of the shemoneh esrei in its entirety. The heicha kedusha method is not recommend for regular use and should only be implemented in extenuating circumstances. This is especially true on Chanuka and Purim when the public recitation of '"al hanissim" is a mitzva in its own right and would not recited out loud as part of the heicha kedusha. The Arizal was very particular to ensure that all prayer services included the full repetition of the shemoneh esrei even if it meant that the repetition of a Friday mincha would extend into Shabbat.
 Tur O.C. 124
 Beit Yosef 232:1
 Although there is reference to a custom of the leader also reciting the last three blessings out loud as well. Biur Halacha 232
 O.C. 109:2,232:1, Kaf Hachaim O.C. 124:10, Yalkut Yosef 1 p.129
 Rama O.C. 109:2,124:2, Mishna Berura 232:8, Aruch Hashulchan 232:3-6, Kitzur Shulchan Aruch 69:6
 Biur Halacha 124:2, Aruch Hashulchan 232:6
 Aruch Hashulchan 232:3-6, Pri Megadim 124:5
 Rama 124:2
 Tefila K'hilchata 13:8, note 18
 Rambam Tefila 8:9, Tur O.C. 124
 Aruch Hashulchan 232:3
 Beit Yosef O.C. 234
 Mishna Berura 124:6
 Tefila K'hilchata 18 note 10
 Kaf Hachaim 232:8