Fortunately for Ben and Polly it's a relatively straightforward issue they stumble into. It's 1600's somewhere in Cornwall, and there are pirates who are in search for a buried treasure. Thus ensues several stereotypes of pirates such as a guy with a hook instead of a hand, but there wasn't a parrot to be found.
There's not much of any weight here. It's basically a pirates buried treasure story but with the twist of the presence of the Doctor. Even that wasn't much of a twist.
The interesting part of this story isn't the story, but that these episodes were nearly the last of Hartnell's tenure as the Doctor.
This was the last story filmed in the third season's production block, although it was intended to be held over until the beginning of the fourth season. During filming, the production team realized that William Hartnell's health had deteriorated beyond the point where he could continue to work. Many months' discussion about replacing Hartnell finally came to a head, and Innes Lloyd decided not to renew Hartnell's contract. It is unclear if Hartnell was contractually obliged to appear in The Tenth Planet or if he agreed to do so after being informed of Lloyd's decision.