Beings who see themselves as the centre of the universe, both literally and figuratively, have a deep propensity for selfishness. This is a point which I will labour a lot because as a starting point, it's not only more solid than the rock of Gibraltar but the rock of the entire continent of Europe. Selfishness not only is the starting point for creatures who have needs and wants but the first motivation for having those needs and wants satisfied and in many cases the last motivation and the only logical endpoint of same.
The human being are unfortunately limited not only by space in that they can only occupy one at a moment but also time in that they can only occupy one moment at a moment. The natural outworking is that we have needs which are time dependent and will with the passage of time tend to become more urgent and wants which might not necessarily be time dependent but come crashing in louder and louder with the passage of time. "I need this" or "I want this" becomes louder and louder with the passage of time as 'eventually' becomes 'soon', as 'soon' becomes 'very soon', as 'very soon' becomes 'now', as 'now' becomes 'NOW', and as 'NOW' becomes 'YESTERDAY IF NOT SOONER'.
Patience then, is either the the discipline of perseverance through waiting through the passage of time, or the setting aside of an immediate desire to have one's needs and wants met immediately; so that 'NOW' becomes 'soon', and 'soon' becomes 'eventually', or possibly 'not at all'. Patience is the turning down of the volume of one's internal monologue to the point where it is not heard, or becomes a quiet whisper in the background.
Neither Aristotle or Plato thought that Patience was a virtue. Thomas Aquinas, on the other hand argued that perseverance is a virtue, albeit a compound virtue which is dependent on other things such as temperance, and courage. I would argue that it is not a virtue at all but a practice and a discipline. The hint to this might be found in the Greek work μακροθυμεῖ - (makrothumei) which means to persevere, to be patient; from makros (increase) and thumos (spiritedness).
Patience has to be cultivated. Or itself, a self which is held inside a meatbag vessel which has needs and wants, would ordinarily demand to be fed now, and/or possibly constantly. Patience is related to things like delayed gratification, self-control and especially self-control over one's own impulses. Patience is if you will, akin to power deferred, or to the saving of hope for later.
We know what impatient people are like. Being impatient has a very marked tendency to demand to elevate the self above all others; so that our needs and wants are met now. Impatience places importance on the self, to the time exclusion of others. Impatience leaves the monster of the self, unchecked, unregulated, uncontrolled and unruly. Part of the job of the training of children to be proper members of society is to bind and chain the monster so that it eventually learns to hold itself in check. What is a 'monster' in botany? It is nothing more than a plant which through disease or injury has grown in an abnormal and usually uncontrolled manner until it no longer resembles the prototypical example of its kind. What is a 'monster' in literature? It is a creature which has grown in an abnormal and usually uncontrolled manner; often from the worst qualities within, such as peoples' fears and cruelties. Patience is very much about holding the monster of the self, still.
Having held the monster of the self still, patience as a moral practice is then turned to the discipline of the self's position within the environment and with other people; which also have needs and wants which can come crashing in louder and louder with the passage of time. We live in a world where things often do not work as we expect, or where tasks have to be done which are time dependent, or when people still act as people and are stupid, obnoxious and/or daft. Patience as the learned and cultivated discipline of perseverance through waiting through the passage of time, makes allowances for other people to act, or accepts that even within a time dependent environment with things all yelling 'NOW', including when those things are of vital importance, holds still.
The moral work here involves reframe the issue at hand. A thing which takes effort also takes thought to prize apart why the thing causes irritation. Maybe this requires the acceptance of a bad thing and even a horrible thing which is unavoidable. Pain, Death and Suffering are three cousins who all like to show up and while the physical effects of pain can be mitigated, the effects of the other two might not be able to be. Very rarely have people been able to make themselves not dead any more. Maybe this requires someone learning to be comfortable in the act of being uncomfortable.
The problem with moral discipline is that it takes effort. Almost similar to longsuffering, patience requires one to accept the circumstances or at very least to make the effort to tolerate them. Those circumstances often include people who are stupid, obnoxious and/or daft, and maybe even deliberately so. Patience is the waiting through without annoyance; without anger; without anxiousness, so that the thing has passed. You very much find that they most patient people have had to learn the skill and have produced patience as a moral product, moreso than patience being a mere by-product if temperament. I do not think that patience is a virtue but rather a quality which should be signalled and practiced.