"Daddy, where are you going?" my son asked me recently as I was lacing up my running shoes on a cold, wet Sunday morning. "Running," I said. "Why?" he asked.

He's only three. But it was a good question, and one I couldn't readily answer. I didn't really want to go. My body was still jarring from the shock of being hauled out of its cosy bed. I was training for a marathon, sure, but it was still months away. Right at that moment, it didn't feel critically important to be heading out into the unruly winter morning. I could go later. Or the next day. Or just not run the marathon. Why was I even running a marathon? But something was making me go. "Because it's fun," I said, rather unconvincingly.

The truth is, just before you run is the worst possible moment to try to explain to someone, or even to yourself, why you run. It just doesn't make sense. Running is hard. It requires effort. And after all the pain you usually end up right back where you started, having run in a big, pointless circle.

Often people say to me they can run if they're chasing a ball, but to just run, nothing else, just one foot in front of the other, well, they find it too boring. I listen and nod, not sure I could convince them otherwise, even if I tried. Running doesn't have logic on its side.

Of course, some people run to lose weight, or to get fit, and these are great reasons. Running is also easy to do, it's cheap, and you can do it when you want without having to book a court or rustle up a team. All these factors certainly contribute to the fact that running is one of the most popular sports in the UK, with more than two million people in England running at least once a week, according to Sport England.

But for many of those two million runners, the real reason we head out to pound the roads until our legs hurt is more intangible than weight loss or fitness. I remember, as a keen runner in my youth, constantly correcting people who asked me if I was running to get fit. "No," I would say. "I'm getting fit to run." I may have thought I was being clever, but for me and many others, running has its own inherent raison d'être. What that is, however, is harder to put your finger on.

Many runners become obsessed with times. The need to break the 40-minute barrier for the 10K, for example, or run under four hours for the marathon, can become the all-conquering reason. There is something reassuring about striving towards such fixed goals, measuring your progress in numbers that are not open to interpretation, but stand there as unambiguous achievements in an otherwise confusing world. Yet, really, these numbers are so arbitrary as to be almost meaningless. And as soon as they are achieved, another target is thrown out almost instantly.

A runner I know last year trained with intense dedication with the goal of running a marathon in less than three hours. In the end he ran three hours and two minutes. Afterwards I spoke to him expecting him to be distraught at coming so close. On the contrary, he was pleased.

"I'm actually glad," he said. "If I'd done it, that would be it. Now I've still got my target, I can try again next year."

No, the times themselves are not the reason we run mile after mile, up hills, in wind and rain, when we could be still cosy in bed, or relaxing with a drink in the pub. The times are merely the carrots we dangle in front of ourselves. We're like little Pacmen chasing PBs (personal bests), gobbling them up before looking for more. But why do we dangle them there in the first place.

"Why do we do this to ourselves!" It's a common refrain at running clubs up and down the country. Usually I hear it as I'm about to head out to run with a group of men and women in fluorescent tops, a sense of foreboding mingling among us in anticipation of the pain we're about to put ourselves through. But nobody ever gives a sensible answer. It's a rhetorical question. Deep down, we all know the answer.

Running brings us joy. Watch small children when they are excited, at play, and mostly they can't stop running. Back and forth, up and down, in little, pointless circles. I remember, even as an older child, I'd often break into a run when walking along the street, for no reason. There's a great moment in The Catcher in the Rye when Holden Caulfield, caught in the uneasy space between childhood and adulthood, is walking across his school grounds one evening and he suddenly starts to run. "I don't even know what I was running for – I guess I just felt like it," he says.

This will to run is innate. In fact, humans may well have evolved the way we did because of our ability to run. Christopher McDougall's bestselling book Born to Run is largely based around a theory devised by Harvard scientists that humans evolved through persistence hunting – chasing animals down until they dropped dead. It's why we have Achillies tendons, arched feet, big bums, and a nuchal ligament at the back of our necks (to keep our heads still as we run). While even Usain Bolt would be left trailing in a sprint against most four-legged mammals, over long distances we are the Olympic champions of the animal kingdom. If they could keep them in sight for long enough, our ancestors could catch even the swiftest runners such as antelope just by running after them.

Indeed, the great Kenyan runner Mike Boit told me the story of how his village held a celebration for him after he won the 1978 Commonwealth Games. He was showing off his medal when his old childhood friend came up to him and said: "That's all very good, but can you still catch an antelope?"

But while as children, and even adolescents, we can respond to this natural urge to run and break into a trot whenever the feeling takes us, as adults it's not the done thing to just start running at any moment, without any reason. So we formalise it. We become runners. We buy running kit. We set out our carrots (our targets), we download iPhone apps, we get people to sponsor us (so there's no backing out), and once everything is set up, finally we can run.

Racing along out on the trails, or even through the busy streets of a city, splashing through puddles, letting the rain drench us, the wind ruffle us, we begin to sense a faint recollection of that childish joy. Somewhere a primal essence stirs deep within us; this being born not to sit at a desk or read newspapers and drink coffee, but to live a wilder existence. As we run, the layers of responsibility and identity we have gathered in our lives, the father, mother, lawyer, teacher, Manchester United-supporter labels, all fall away, leaving us with the raw human being underneath. It's a rare thing, and it can be confronting. Some of us will stop, almost shocked by ourselves, by how our heart is pumping, by how our mind is racing, struggling with our attempts to leave it behind.

But if we push on, running harder, deeper into the loneliness, further away from the world and the structure of our lives, we begin to feel strangely elated, detached yet at the same time connected, connected to ourselves. With nothing but our own two legs moving us, we begin to get a vague, tingling sense of who, or what, we really are.

In Japan, the monks of mount Hiei run up to 1,000 marathons in 1,000 days in an attempt to reach enlightenment. I once stood by the roadside at around mile 24 of the London marathon, watching as person after person ran by, almost every one of them at a point in their lives they would rarely visit again. It was almost like seeing into their souls, their faces grimacing and contorted, but also alive with the effort. Each one of them soon after crossing the line would be glowing with a sense of wellbeing. Some may even be moved to tears by it (I was after my first marathon). It's the fabled runner's high, of course, but by labelling it such we diminish it. It may only be chemicals shooting around in your brain, but after a long run everything seems right in the world. Everything is at peace.

To experience this is a powerful feeling, strong enough to have us coming back, again and again, for more.