This is a very broad question as it depends on region, time, subculture and to an extent individual preference. Because I really should be doing work for the start of Michaelmas I am going to limit to a particular example/period - the British upper class in the inter-war years. Indeed, I am going to focus on one individual as a kind of case study.

This is where our protagonist steps in, Austen Chamberlain, son of arch-imperialist, party-shifting and also be-monocled Joseph Chamberlain and half brother of Neville Chamberlain.

Now obviously by this point glasses existed, however in Britain in this period they were slightly tainted. First by the debates on 'national efficiency' during the turn of the century (the closest British politics meaningfully got to domestic eugenics) where poor eyesight, and therefore glasses, were seen in some quarters as symptoms of degeneracy, though more on a social rather than a personal (i.e. burn the broken eyes!) level. Second they were tainted with a whiff of plutocracy and or Liberalism/Fabianism in certain circles.

This leads to your question and provides a few inevitably interrelated issues. First the utility of the monocle is very mixed. It can be argued that in Britain it was a signifier for identity as opposed to a mechanical eye-correction. Heneta goes into wonderful detail about the cultural iconography of the monocle across regions and periods which is very helpful to explore periods and countries where I lack specialism. Broadly, in the culturally-disciplined class hierarchy during British Edwardian/interwar period the monocle was a sign of rarefied aristocracy. It was more narrowly and rigidly confined by social convention than other countries. Even the occasionally be-monocled Bloomsbury Group of artists and writers were generally of a 'respectable' background. Cannadine argues that faced with their precipitous (though many question this characterisation) decline economically and politically the British aristocracy tended to 'retreat' into this iconography of elitism, from sumptuous feasts to countless dances to elite education to well heeled Saville Row attire (the cost of which arguably only worsened the underlying issue). These were essential to clinging on to notions of aristocracy when social mobility (and slipping) were shifting Britain's centre of gravity and the upper echelons were being 'diluted' by a newly prosperous class of "hard-faced" people who could now 'buy' there way into the haunts and, in some cases, families of the old aristocracy.

It was important to maintain (or assert) one's social standing through these trinkets, one of which was the absence of glasses/presence of a monocle. Indeed Joseph Chamberlain, a (self-)consciously self-made man (as much as one was in the era) was rumoured to not even need his, however whether this is actually true is still debated and there is a good chance this is a character assassination by right-leaning colleagues as opposed to historical fact. But nonetheless that fact that this is even a thing suggests a lot, a failure to need a monocle/unnecessary use of one effortlessly and in unspoken tongues being linked to issues of class.

So we have an object which in the curious class conscious Britain during the early 20th century is a talisman as much as a tool. Step in our protagonist, now he really needed glasses. His left eye had been damaged at school, but fortitude and the potential stigma of correction for a son of Joseph Chamberlain who wanted to follow in his father's footsteps forestalled any. He then developed shortsightedness in his right eye. Now herein lies the problem. This is the 1918 coalition front bench these are the 1906 largely Liberal welsh MPs, hell this is the pre-war Labour bench, a party whose relatively unhealthy proletarian upbringing will mean that the average Labour MP will be notably shorter than his well fed Conservative cousin for half a century until they finally catch up. The similarity? - spectacles are really out of fashion before the 1930s (many of these men needed them but went without them or wore them in private), and even then they will only creep in slowly, particularly amongst the left (now that is a whole interesting separate issue about why there was a shift towards acceptance of glasses amongst Labour men).

So the only option for Chamberlain was to wear a monocle. However, the monocle is not the best for actually seeing in. While it helps distinguish objects et al and make functioning easier fine detail was not great - particularly in Chamberlain's case with his very poor eyesight. So why is this interesting? Because arguably this decision shaped the future of British politics.

Austen was inevitably the leader of the Conservatives following Bonar Law's resignation on grounds of ill health in 1921. Law had only beaten Chamberlain last time round as he had been a compromise between the free-trade and the protectionist wings (Chamberlain) of the party to keep the peace after Joseph Chamberlain's political kamikaze over the issue. By the 1920s protectionism reigned supreme and Austen was firmly in line for leadership. This was a crucial time for British politics. The best and most effective (if amoral and amorphous in his politics) PM in the early 20th century, David Lloyd George, was in power in a coalition with the Tories after abandoning his party. He had been in turn abandoned as a traitor by the rump of his old Liberal party and was in the process of attempting to create a new centrist party combining the right of the liberals and left of the Conservatives as a bulwark against socialism. If anyone could have managed this it would have been Lloyd George, it was also the only way Liberalism could realistically be saved. However while Law and the cabinet were supportive the backbench Tories started to chaff under this arrangement by 1920. Now to be a good Tory party leader you need to be able to manage your backbenchers. It is a party which is an absolute monarchy, governed by regicide. Law was good. Chamberlain, though a little awkward, could have been fine. Except he had difficulty even seeing his MPs in the Commons tea rooms, even close up. This made working the room hard, and even an acknowledgement of his juniors across scones impossible. I cannot overstate how important this skill is in British Parliamentary politics during this time. Baldwin, Chamberlain's successor, despite being largely devoid of ideas, oratory or inspiration built a highly successful career on being 'clubbable' and his ability to smoke with even opposition, and (kind of) proletarian, Labour MPs (on their pipes, obviously, they are Labour after all (GOD I love this period)) in the tea rooms of power - something learned from the paternalist approach of his family's manufacturing business. Lord knows Chamberlain knew what he had to do, and wanted to, but he couldn't as he could not see them. The result? Despite so many in the party wanting to like him because of his protectionism, intellect and pedigree (and guilt over what happened to his father), Chamberlain very quickly gained a reputation for aloofness. This is fatal in Tory Parliamentary circles, particularly when mutiny is in the air. Without getting too far on a tangent it led to increasing dissatisfaction culminating in an unprecedented mutiny against Chamberlain at a Parliamentary party meeting in the Carlton Club in 1922. This directly caused the breakdown of the coalition, resignation of Chamberlain, the end of Lloyd George as a PM and political force forever, (and a little more debatable) the ended the last great hope of the saving British Liberalism, the fallout of this helped engender two Minority Labour governments, and led to the creation of the modern Conservative-Labour dichotomy. Pretty cool in terms of unintended consequences.

Tl;dr: in early 20th century Britain it was as much a talisman to denote what you were and were not massively helpful as a practical corrective of eyesight. Plus me nerding about Austen Chamberlain for half the post.

Sources:

Cannadine, D. (1990). The decline and fall of the British aristocracy. New Haven, Conn.: Yale University Press.

Clarke, P. (1996) Hope and glory: Britain 1900-1990. Edited by David Cannadine. New York: Allen Lane, The Penguin Press.

Dutton, D. (1985). Austen Chamberlain, gentleman in politics. Bolton: R. Anderson.

Hentea, M. (2013). Monocles on Modernity. Modernism/modernity, 20(2), pp.213-237.

Pugh, M. (1994). State and Society. London: E. Arnold.