As you might expect, the average (always a tricky concept, that) officer in the American or British armies will have a VERY different answer to this question, so much so that it's practically a different question. I'll tackle the Americans first, and will swing back around to the British in a separate comment if no one more qualified comes along.

American junior officers generally operated in a peculiar social framework. They tended to be young and of the middling sort - no great surprises there. Across the colonies, but particularly in New England, men of this generation and condition tended to be stuck in a bit of a rut. Nearly all the land in the most densely populated parts of the colonies - the places with the best access to the Atlantic - was owned by their parents' and grandparents' generations. Due to a number of factors, these generations lived longer and more productive lives than their predecessors, depriving the 20somethings of the colonies a chance to inherit property. This meant that the future young officers of the Continental Army had to wait around until their mid-late 20s or early 30s, during which time they depended on their parents financially. This was a deeply embarrassing situation for a man to be in, according to the cultural and gender norms of the time. Military service provided a useful way out of this jam. The pay, position, and land grants offered with or accessible through joining the army offered a shot at at financial independence. Since Continental Army units were recruited locally - usually one or two counties fed into one regiment, at the largest - it also allowed these young men to spend a time previously marked by stagnation and dependence to start building an independent reputation and assuming positions of prominence in the community.

Once in the army, success was built both on social skills and technical proficiency. Let's talk proficiency first. Very few junior officers entered the service with any kind of military experience besides militia drills, and there was no formal training program for officers. This meant that a great many officers had no real idea what they were doing. Fortunately for the most dedicated among them, the 18th century was the age of the military treatise, and foreign observers repeatedly noted that American officers were voracious readers. Available works covered everything from how to conduct oneself as a gentleman to the finer points of ballistic physics. Demonstrating competence in basic personnel management during the wide array of tasks infantry troops could be assigned was a good way to get noticed. The ability to read and write well could earn one a staff position, and access to rapid promotion (all of Washington's aides were in their early 20s, yet were full-bird colonels). Bravery and coolness under fire was, of course, the best way to make oneself famous, but that rested upon actually seeing and surviving combat and finding an opportunity to get oneself noticed. Doing well in combat and being physically fit enough to keep up could lead to a transfer to the light infantry, an elite corp who handled the hardest - and thus most talked about - fighting. Serving in a "forlorn hope" - the advance wave of an assault on a fixed position - was a good, if HUGELY risky, way to earn attention and commendation, as was being the first person into an enemy defensive work. Capturing a gun, prisoner, or supplies also added a nice feather to one's cap. There is a story, documented in the period but never with any names attached, of two lieutenants at Cowpens (I think) racing each other to be the first to lay their hand on a British cannon during a charge. Supposedly, the winner achieved victory by using his spontoon as a pole vault. This is almost certainly fiction, but it does illustrate the focus on prizes and the honor of being first.

Arguably, both Continental officers and modern scholars paid more attention to the social dynamics of being an officer. In organization, dress, and demeanor, the Continental Army modeled itself after the British army and the other standing armies of Europe. This meant that there was a wide social divide between officer and enlisted. In Europe, this was easier to maintain: commissions were generally kept to those with money or titles, and these people often had great physical or social distance between them and the poorer sort that made up the enlisted ranks. This was not true in the junior ranks of the Continental Army. The local nature of recruitment meant that men generally served with men they knew, and the economic gaps for those entering military service weren't anywhere near as large as they could be in other armies. This meant that childhood friends and acquaintances now had to call one of their own "sir," and accept that he had the power of life and death over them. You could imagine that this was often an awkward, contentious process. In order to establish their authority, many junior officers were very picky about being addressed with all the honors and distinctions due to their ranks, and were quick to resort to physical violence to compel deference. Those that could maintain good order, discipline, and deference - with or without violence - were generally considered good officers, while those that drank, brawled, or gambled with enlisted men could find themselves reprimanded or cashiered for conduct unbecoming an officer. Successful officers also knew how to carry themselves in polite company and amongst their betters. Every army camp featured officers-only parties and dances where generals and ensigns mixed side by side in the pursuit of eligible young bachelorettes (or bored and lonely ladies). Washington made it a point to invite the previous day's officers of the day - those tasked with the basic administrative and security jobs around the camp - to dine with him at least during the winter of 1780-81 (he probably did this elsewhere. I just need to read up on it). A bumbling performance of uncouth remark in these arenas could make one a social outcast or get one challenged to a duel.

Sources

Carolyn Cox, A Proper Sense of Honor

Gregory T. Knouff, * The Soldier's Revolution*

Charles Neimeyer, America Goes to War. A Social History of the Continental Army

Charles Royster, *A Revolutionary People at War.