If you trek somewhere, you go on a journey across difficult country, usually on foot. trekking through the jungles This year we're going trekking in Nepal. Trek is also a noun. He is on a trek through the South Gobi desert
any long and difficult trip a journey by ox wagon (especially an organized migration by a group of settlers) make a long and difficult journey; "They trekked towards the North Pole with sleds and skis"
If you trek somewhere, you go there rather slowly and unwillingly, usually because you are tired. They trekked from shop to shop in search of white knee-length socks