Hah! I thought Zenda had already explained it much better than me!
In a nutshell, it's simply to stop being subject to any kind of suffering, no matter how subtle it might be. And note that even what we usually see as happiness is not "perfect": after all, a moment of happiness (no matter how long it can last) will end at some point in time. Even if it ends with one's death

And when that moment passes, we will wish to feel happy again and do our best to do so — this is a subtle form of unhappiness. What meditation techniques achieve is to simply deal with all that confusion about what makes us suffer and what makes us happy, and erradicate the root of all suffering, once and forever, so that there is not any other single moment of unhappiness. Ever. Again.
You might say that this is an impossible goal — but it's not, it's just
very hard. And, while on the road to achieve that, you still get all the benefits from the "side-effects". These will just improve over time, but if one only meditates to achieve those benefits, well, then the same kind of subtle unhappiness steps in. Imagine someone who meditates to feel a bit calmer. That's fine by itself and a good start. However, once you stop meditating, the effects of that calmness, like everything else, will slowly fade away. Obviously, the more you train, the longer the effect will remain, but it will
still fade away.
So this has several consequences: the first one being, "why bother?" As you so well put it, a few beers will also "calm" you down (at least, for some people, alcohol has a calming effect — it's certainly my case!) and won't require any training whatsoever. This might be discouraging for some — I've came across a couple of people who told me things like, "oh, meditation. I did that for ten (or even twenty) years and I'm still a stressed person. It helps a little to calm me down, but legal drugs are much better." That's a typical case of someone who focused on the side-effects of meditation while forgetting the ultimate goal.
The other possible consequence (albeit a rare one) is becoming obsessive about meditation, in the sense that it evokes some "good feelings", so you'll do it more and more to feel those "good feelings" (whatever they might be: calmness is an example). But since the motivation is all wrong, the result will just be getting a new obsession, and all the psychological complications resulting from an obsession. This is why it's important to get a qualified teacher that is able to point the way ahead while still warning about the pitfalls!
Another consequence, which is not so rare, is simply getting an ego-boost which will spoil the whole training: "oh, I'm such a spiritual person, I do a lot of meditation, and I'm so much better than the other people, who do nothing to improve themselves". Anything that provides an ego-boost is radically opposed to the whole concept :-P But unfortunately this is something that is quite common; it has even a technical name, coined by Chögyam Trungpa:
spiritual materialism. It's typical for a certain class of people, who have little success in mundane endeavours (i.e. they might have a lousy professional career, or utterly fail to raise a family, or fail to pursue any worthwhile goal in life to be admired by others), and, at some point, they decide to become "spiritual" in an attempt to "show off" something that they're good at. Unfortunately, this is a very common trap, and, sadly, a lot of New Age groups actually promote this kind of mentality! And this will ultimately not only not benefit the person by themselves, but also make them get shunned by their friends and colleagues: let's be honest, nobody likes people with "holier-than-thou" attitudes :-P
A subtle form of spiritual materialism can be excessive, fake modesty: people claiming that they're completely worthless, the worst of the worst, and adopt an attitude of humility and submissiveness that is frankly irritating, in a deluded attempt to validate their interest in meditation — thinking that meditation should turn them into meek, subservient beings, and that by "showing off" how meek and humble they are, they're "revealing" their "spiritual prowess". While, in fact, this is just a different form of ego build-up, but in reverse — it's a mentality to compete to become "the worst of the worst".
Rather, a meditation practitioner will certainly develop a certain amount of humbleness — while they evaluate the degree of achievement in their training, compared to their own teachers, for example — but, at the same time, they will build up some confidence that: a) it works; b) we all have the ability to train ourselves, so that doesn't make us "special", but it simultaneously avoids thinking too bad about ourselves. It's a bit like driving a car: it's hard at the beginning, it's easier for some than for others, but, with enough training, we can all drive cars. We're not really "special" for being able to do so, but neither are we morons if we take longer than others — each of us is different.
I'm sure that there are a lot of other good examples about what happens when one focuses on the side-effects of meditation instead of the ultimate goal, but these should give you an idea

Nevertheless, it's also true that most people get "attracted" to meditation because of its positive side-effects. There's no harm in that by itself: if meditation was something horrible and stressy and uncomfortable, only masochists would try it out

So, sure, the list of benefits from meditation
is important. They are also a good sign that the practice is in the right direction. Qualified teachers will often tell their students to ask themselves: "am I a more level-headed person? do I behave in a more functional way? am I able to deal better with extreme emotions, from anger to euphoria?" If yes, then that's a sure sign that things are progressing in the right way, and the easiest way to know you're doing something right is if you can experience any of the side-effects. But one should not get side-tracked!
This is the reason why I frown a bit when seeing claims that meditation is able to develop extraordinary powers like mind-reading, levitation, or walking through walls. What my own teachers say to that is simple: if you're feeling very depressed, what use is to be able to walk through walls? (The ones with a keener sense of humour even add: anyone can walk through walls, all they need to know is how to open the door!)
Similarly, it's great if you're able to feel calm
during meditation, but if at your workplace a colleague suddenly pisses you off and you angrily yell at him or her — what's the whole point? You can even claim to meditate hours upon hours every day to "feel calm", but if you still can't remain calm when people yell at you, then something is simply wrong. And, unfortunately, I'm aware of lots of people like that. One good friend of mine, for example, is always boasting on Facebook about how she has already bought "the whole meditation kit" and does I don't know how many minutes of meditation every day. But every second message of her on Facebook is about how sad and depressed she feels, often being unable to leave home for work. I have no idea who taught her meditation, but I'm pretty sure it wasn't a qualified teacher, but just a book she read, or a tutorial she followed, without guidance. And I'm also pretty sure that in a few years she'll give it up and say, "meditation didn't work for me; I need drugs to deal with depression".
That's just because she was missing the whole point — not her fault, but very likely the fault of whoever told her about meditation (be it a book or a human being).