Now chiefly used to mean absurd; ridiculous.
I know that this site generally deals with phrases rather than single words, but this word packs in enough to be counted as virtually a phrase. We may go through life using 'preposterous' as a synonym for 'absurd; laughable; ridiculous' without giving any thought to why it means that. By breaking it into its constituent parts it becomes clear that its meaning can be read quite literally, i.e. it describes something in which the 'pre' (front) has become the 'post' (rear). So, 'preposterous' things or, more usually animals, were those which were contrary to nature; having their parts in the wrong order.
A mediaeval belief in the existence of monstrous or fabulous animals was commonplace, indeed almost universal. To the usual collection of dragons, griffins, mermaids, unicorns and the like we can also add animals that had their heads and tails reversed and those which had heads at both ends, for example the Amphisbaena.
The use of 'preposterous' to refer to things which were wrong or inverted dates from 1533, when it was so used several times in a translation of Erasmus' Enchiridion Militis Christiani. The use of the term to refer specifically to 'wrong' animals was in use by at least 1661, when it appeared in Joseph Glanvill's The Vanity of Dogmatizing:
"Thus our Eyes, like the preposterous Animal's, are behind us."
See also: 'Lick into shape'.