Wikipedia has a nice summary of the aorist here and more details can be found here.
This is from the first link.
In the Ancient Greek, the indicative aorist is one of the two main
forms used in telling a story; it is used for undivided events, such
as the individual steps in a continuous process (narrative aorist); it
is also used for events that took place before the story itself
(past-within-past). The aorist indicative is also used to express
things that happen in general, without asserting a time (the "gnomic
aorist"). It can also be used of present and future[7] events; the
aorist also has several specialized senses meaning present action.
Non-indicative forms of the aorist (subjunctives, optatives,
imperatives, infinitives) are usually purely aspectual, with certain
exceptions including indirect speech constructions and the use of
optative as part of the sequence of tenses in dependent clauses. There
are aorist infinitives and imperatives that do not imply temporality
at all. For example, the Lord's Prayer in Matthew 6:11 uses the aorist
imperative in "Give (δός dós) us this day our daily bread",[8] in
contrast to the analogous passage in Luke 11:3, which uses the
imperfective aspect, implying repetition, with "Give (δίδου dídou,
present imperative) us day by day our daily bread."[9]
An example of how the aorist tense contrasts with the imperfect in
describing the past occurs in Xenophon's Anabasis, when the Persian
aristocrat Orontas is executed: "and those who had been previously in
the habit of bowing (προσεκύνουν prosekúnoun, imperfect) to him, bowed
(προσεκύνησαν prosekúnēsan, aorist) to him even then."[10] Here the
imperfect refers to a past habitual or repeated act, and the aorist to
a single one.
There is disagreement as to which functions of the Greek aorist are
inherent within it. Many authors hold that the aorist tends to be
about the past because it is perfective, and perfectives tend to
describe completed actions;[11] others that it is essentially a
mixture of past tense and perfective aspect.[12] [edit] Hermeneutic
implications
Because the aorist was not maintained in either Latin or the Germanic
languages, there have long been difficulties in translating the Greek
New Testament into Western languages. The aorist has often been
interpreted as making a strong statement about the aspect or even the
time of an event, when, in fact, due to its being the unmarked
(default) form of the Greek verb, such implications are often left to
context. Thus, within New Testament hermeneutics, it is considered an
exegetical fallacy to attach undue significance to uses of the
aorist.[13] Although one may draw specific implications from an
author's use of the imperfective or perfect, no such conclusions can,
in general, be drawn from the use of the aorist, which may refer to an
action "without specifying whether the action is unique, repeated,
ingressive, instantaneous, past, or accomplished."[13] In particular,
the aorist does not imply a "once for all" action, as it has commonly
been misinterpreted.[14]
