We've talked a lot about the various formations teams can use, but what we haven't discussed is why they really matter. The why is pretty clearly the keystone in examining how things all work - you can't understand the flaws in a 4-4-2 without some understanding of what causes imbalances in a shape in the first place. So instead of simply looking at shape from the 'hey I know what that looks like' perspective, let's push for something a little deeper. This is just a quick sketch of my thoughts on the matter, but I hope it's enough to at least start a decent conversation...
In football, you seek to score more goals than the opposition. That's the basic goal. In general, this is accomplished by outplaying the opposition, and that play can be broken down to dominance of one team over another in specific zones of the pitch.
I like thinking of a football field as having seven major areas - central attack, central midfield, central defence, and two wide attacking and defensive zones. Your mileage may vary. It's obvious that certain zones are more important than others, and that the relative weighting changes depending on the situation - if your team is 6-0 up suddenly the central attacking zone loses all of its importance , but if you're 1-0 down in the 90th minute, you're often willing to desert your own defensive zone to put a goalkeeper in the opponent's half. The actual weighting of these zones isn't really very relevant to a big picture analysis, but it's very important that we accept that it's a situational property than can change based on the state of the game or even the composition of the team.
Control of these zones can be undertaken in a number of ways, but the two obvious answers are to either be better than or outnumber your opponents. It's obviously a zero-sum situation here, as the opposition will be trying to do exactly the same thing back to you. Outplaying the opposition isn't really a matter for tactics - the need to be better is not a profound piece of knowledge. However, outnumbering the other team in specific zones lies solidly in the realm of tactics, because you primarily make gains by tweaking team shape.
But there's a problem. There are ten outfield players available to managers for each team, and to outnumber the opposition in one zone another has to be weakened. You cannot commit to all-out attack without damaging your defence in return, and that then becomes something for the other team to exploit. Shapes, then, follow the weighted value of certain areas of the field for a specific team.
This is a pretty big concept, because it means that every formation is the expression of certain values. 4-4-2's great strength lies in the two strikers up front, which allows them to contest the central forward zone very effectively - but they weaken their central midfield zone to do so. The opposite is true of, say, a 4-5-1. At the end of the day, shape is simply a team's answer to which areas of the field they care to control.
We must remember that football teams often do not know what's good for them, and as they learn to answer that question better tactics tend to evolve. Football is currently in an era where possession and passing dominates, which often leaves teams with strong central midfields in better position than those without (hence the rise of 4-2-3-1 systems over 4-4-2). This specific pattern may not continue, but as long as you can read trends and translate them into values on the pitch, you'll never have a problem understanding the intricacies of team shapes.