Every Whovian has been in the situation before of trying to explain the premise of Doctor Who. And beyond explaining the premise of the show, there is also the perennial question of its genre. It is usually described as a "science-fiction" show, although it could better be described as a fantasy. Its plots can vary between space opera and gothic horror, and it can be a dialogue-heavy comment on society, or an action-filled adventure.
Many of the templates for Doctor Who stories were already being established in the first season. "The Keys to Marinus" is significant as the first Doctor Who story that was written and filmed as an adventure story. The two previous stories had been the tense psychological thriller "The Edge of Destruction", and the long, slow paced political story "Marco Polo". And then we are dropped into this: a quest for McGuffins across an alien world full of murderous plants, nefarious trappers, brains in vats, scuba-diving amphibians, acid seas, suspiciously happy societies, a locked room mystery, spelunking, and a Perry Mason style courtroom drama. This is the first example of the great Doctor Who principle "If something doesn't make sense, throw in other things that don't make sense until it does."
And although the writing, special effects and production values might seem a bit hokey today, its is a very enjoyable story when viewed in the light of being a prototypical adventure story. Because The Keys of Marinus is basically Doctor Who doing a matinée serial-type adventure. By the next episode, The Aztecs, the show would be back to a serious lesson on hubris and the impossibility of changing history. For "The Keys of Marinus", it was time to enjoy running, fighting, and clever escapes.