Let's start with hardy - that's an easy one. A hardy plant is one which will withstand extreme cold, winds and frost. In your veg garden, this would be the likes of savoy cabbage, cavelo nero and overwintering broad beans.
Now it starts to get bizarre. Any normal person would expect half hardy and tender to operate on a sliding scale towards wimpishness in the face of harsh weather conditions. But no, that would have been far too straightforward and intuitive. Instead of which, tender is used to describe a plant which may be killed by a frost and half hardy is the term applied to a plant that will certainly end its days if confronted with a below zero temperature.
Logical? Hardly! I'm sure that's been confusing the amateur gardener as far back as the advent of the max/min thermometer. To whoever makes up these terms, can I suggest something? Next time you're dealing with a plant lacking in the cellular and substantive fibre to stand up to a bit of chilly weather, try leaving the word hardy out of it.