Detours are the areas in a mystery dungeon found behind gates, vines, ice, or poison gas. When it says you recieved (Pokemon's name) telepathy, theres a detour near you, that means you are on the same exact floor the detour is on. You need a key to open the gates, but the key needs to match the color of the gate. EX: Red gate is opened with red key. The ones behind vines ice and poison don't need a key.
Edit: Vines are possible to get rid of with a grass type. You need a poison type for poison gas and you need an ice type for the ice. Also there are golden P gates, where you need a certain amount of P to open them.