How does a dweller "explore 1 location in the wasteland?"

This is a reference to the random encounters that happen to Wasteland explorers. You have to have an Overseer's office (any level) to get them. They only come up while the game is running; they will not happen once you exit. There's a morse-code-sounding noise when they come up, like a radio transmission, and the icon to either Enter or Ignore it appears below your dweller number gadget in the upper left of the user interface. You do NOT have to have built a radio station. The objective is completed once you return the explorer to the Wasteland; you don't have to wait until they come back to the Vault.

Trying to be as spoiler free as possible here:

Once your dweller has explored for a period of time (it can be from 1 minute to many many hours) then they may 'discover' something in the wastelands. This discovery (and their safe return I presume) will complete this objective.

If your dwellers aren't yet up to this challenge it maybe worth just recycling it into a different objective for the time being.