The name ‘participle’ means ‘something that takes part’. That’s not really helpful. What it does is this: It behaves like a verb, as it can express tense and voice and can govern objects and a subject. But it also behaves like a noun in a broader sense (including adjectives), as it expresses gender, case and number. As every verb implies a clause or something like a clause, you can effectively express two states of affairs in one main clause.
The supine is rather obscure and not used very much. The most common expressions with it are probably mirabile visu ‘amazing to look at’ and difficile dictu ‘difficult to say’.