In some circles, an ornament means a useless figurine in a windowsill or on the mantlepiece. Conversely, ornamentation means everything that decorates, adorns, or embellishes in art and achitecture.
In popular usage, ornamentation means all things ornamental and it has been with us right from the earliest civilisations. But the etymology of the word ‘ornament’ is much younger. Ornamental and ornate refers to a particular style of fresco painting in classical Rome and does not have any real connection to today’s popular usage of the words.
Today ornamentation is somewhat synonymous with decoration used for purely decorative purposes. It refers to e.g. the embellishment of a building or object and is an integral part of our visual culture. Indeed attempts to strip visual art ornamentation is not only dull but is also near impossible. Even minimalist art has plenty of it even if it is unintentional.
Ornamentation plays an important part of any medieval manuscript as does whiplash curlicues in art nouveau poster art. Ornate patterns are strongly linked to the arts and crafts movement and so on and so forth. There are many types of ornamental styles, and some are clever mathematical and geometric shapes as is much the case in Islamic art. Others again use nature or natural shapes such as foliage.