Three years ago, in a garden full of cypress trees, I watched men and women kissing a marble tomb. Some of them were smiling. Some were wiping tears away. Nearly all of them where whispering words that sounded like a prayer, or song. But the words they were reciting, in this beautiful garden, in Shiraz, in Iran, weren't the words of the Koran. The words they were reciting were the words of a poet born in Shiraz 700 years ago called Hafez.

If you grow up in a country like England, where poetry is something most people study a bit at school and then forget, it's quite a shock to see poetry have so much power. You know, in theory, that it can. You've heard about the poets who filled football stadiums, in Russia, and Eastern Europe. You may even, like me, have met quite a few of them, and heard them read, and talk about, their poems. But it's still a shock to see men, with moustaches, and women, in chadors, fighting tears, as if the words they're reciting are written on their hearts.

So when I heard there was going to be a tour of Persian poets in this country, I wanted to find out more. It's nearly a decade since I ran an organisation promoting poets and poetry, and since I talked, publicly and often, about poetry's role, and power. I wanted, in an age when we get our entertainment at the click of a mouse, to be reminded that poetry can matter. To see if I still believed it could.

"I think," said the poet Sarah Maguire, at the launch of the Persian poets tour, at an art gallery in Bloomsbury last week, "that what you experienced in Iran you'd also experience in Afghanistan, Tajikistan, Somalia or Sudan. Poetry in these countries is of overwhelming importance. Both Arabic and Persian culture have this very old, pre-Islamic tradition of written poetry. In Somali culture, it's oral. The most poetry-obsessed people in the world are Somalis." I knew about the Arabic and Persian obsession with poetry, but I didn't, I told her, know about the Somalis. But Somalia is as near to a failed state as you get, and only an Ayatollah could claim Iran was a successful model of anything much. So what, exactly, is gained?

Maguire was quiet for a moment. "I think," she said, "it's the people's pride. Somalis are the most traduced and stepped-on people on Earth, but they have this sense that their identity is carried by poetry. One of the things I wanted to do in setting up the Poetry Translation Centre was to try and get across to British people that there are these people here who may be at the bottom of the social pile, but have this extraordinary tradition of rich culture, and this dignifies them."

But isn't poetry a bit of a luxury when lots of very poor people are having their meagre incomes cut? Why should we pay to hear work by foreign poets we've never even heard of?

"Because," said Maguire, "it makes a huge difference to people here. The reaction we have at our events is just extraordinary. It has a knock-on effect. Particularly given the whole attitude of the "war on terror", and this hostility to Muslim cultures. We can say, 'these people are a hell of a lot more complicated than you think they are'."

This, it turns out, was the lesson learnt by the five British poets who worked with Persian scholars to translate the work of the poets on the tour. Jo Shapcott, who's representing Britain at the poetry strand of this summer's Cultural Olympiad, and who has translated poems by Tajikistan's leading poet, Farzaneh Khojandi, said there was a "huge cultural gap" she needed "not just to negotiate, but leap". There were, she told me at the launch, "huge frames of reference" that were entirely new to her, like "the world of Zarastra," which is central to Persian culture, and the "religious ideal".

"These are poems," said Shapcott, "by someone who doesn't have electricity all day long, and who can't travel to get a visa because there's not much transport, and the snow is too deep. So the poems are written out of a fiercely idealistic spirit. It's a real lesson to Western people. She's writing about love, and passion, and literature, and thinking as a great mind, but as a great mind who doesn't have stuff."

Farzaneh Khojandi wasn't the only poet who didn't make the tour. Partaw Naderi, who spent three years in prison in Kabul under the Soviet regime , also couldn't get a visa. The three who did make it are the ones who live in the West. I met them on the first day of their tour, at a flat in West London.

Shakila Azizzada left Kabul for the Netherlands 27 years ago. She left, she told me over cardamom tea, after being arrested several times, when she realised it was "too dangerous" to stay. She was, she said, "more comfortable" with the Dari language (the Persian spoken in Afghanistan) now than when she was there. It had, she said, been "necessary" to "hide meanings in some words", saying, for example, "green areas", not "freedom".

Reza Mohammadi grew up in two of the three countries where Persian is spoken, Afghanistan and Iran. He's now a journalist in London, but misses Afghanistan and wants to go back. He hopes, he said, to go back next year to build a school in the village where he grew up.

Azita Ghahreman is from Mashad, in Iran. She's one of five generations of women poets in what used to be the Iranian royal family. After years of writing under censorship, she went, six years ago, to live in Sweden. She doesn't, she told me, miss the censorship, or the regime, but her poems are full of yearning for the culture she left behind.

"When we read The Shahnameh," she said, meaning the 1000-year old epic poem by the Persian poet Ferdowsi, "all of the people of Iran, and Afghanistan and Tajikistan understand. We can find common things about love, happiness and war. These books are the memories of humans on the Earth."

Poetry, it's clear from these remarkable poets, can be central to a nation, and a culture, and a life. It can, as Maura Dooley, who translated Ghahreman's work, explained, "offer a tiny window into another person's way of understanding the world".

In the end, the poems must speak for themselves. If you read them, in these brilliant translations, done by brilliant poets, working with brilliant scholars, you'll find they do. You'll find they speak, as all art should speak, of love, and life, and loss. You'll find yourself thinking of the corn poppies that used to bloom before the shadow cast by "the mountain range of a thousand mosques". You'll find yourself thinking of "the last bird of the garden," and of the winter that has passed. You'll find yourself thinking of stars that "rise from the blisters on... hands," and desperately hoping they do.

The Persian poets' tour runs until 21 May. www.poetrytranslation.org

Excerpt from 'Glaucoma' by Azita Ghahreman