Why did Matsuo Basho travel?

Your question is about Matsuo Basho's purpose for traveling as described in The Narrow Road to the Deep North. 

Matsuo Basho was possibly the son of a samurai of low rank. He worked as a servant to a man named Yoshitada; they shared a love of a type of poetry called hokku (which would later be changed to haiku). While Basho might have grown to be a samurai, Yoshitada's death caused him to leave home and seek his fortune elsewhere in the world.

Basho became a notable poet and teacher. After he sold his home near Tokyo, he decided to travel for months at a time. There was no specific purpose for his travels beyond that of a spiritual journey and a deep desire to travel.

Near the beginning of The Narrow Road to the Deep North, Basho writes: 

Only last year, I had been wandering along the coasts and bays; and in the autumn, I swept away the cobwebs from my tumbledown hut on the banks of the Sumida and soon afterwards saw the old year out. But when the spring mists rose up into the sky, the gods of desire possessed me, and burned my mind with the longing to go beyond the barrier at Shirakawa. The spirits of the road beckoned me, and I could not concentrate on anything. So I patched up my trousers, put new cords in my straw hat, and strengthened my knees with moxa. A vision of the moon at Matsushima was already in my mind. I sold my hut...

For Basho, spirituality was about both expanding his own understanding of the world and finding new and better ways to write his poetry. Basho yearned to travel. He saw life as a journey. His travel allowed him to expand his own understanding of the world, see the beauty of nature and people, and use those things in his own writing.

His journeys weren't planned like clockwork. He went where he chose, sometimes visiting friends for stretches and other times just stopping to see a point of interest. Basho was inspired by the natural beauty of Japan as he traveled, and he wrote many poems expressing his reaction to the sights around him.