There are two unrelated uses of
elative in
linguistics. As a
case marking on a noun, for example in
Finnish, the elative case indicates motion
out of somewhere. It is the opposite of the
illative, which marks motion into.
When referring to adjectives, it means an intensive form that can be used for both the comparative and the superlative. In English there are distinct inflected forms for comparative bigger and superlative biggest. A language with an elative has a single form covering both.
In Arabic elatives have the vowel pattern ?aCCaCu (masculine) and CuCCaa (feminine), so from kabiir 'big' we get ?akbaru and kubraa, which mean bigger, biggest, or very big. The word min 'from' is used as the equivalent of 'than': ?inna-l-walada ?akbaru mina-l-bint 'the boy is bigger than the girl'. With no object of comparison, ?inna-l-walada ?akbaru means 'the boy is biggest' or 'the boy is very big'. Equivalently, you can compare him to 'all' or add al- 'the' for an explicit superlative meaning.
The Arabic word kabiir means abstractly 'great' as well as physically 'big', so this construction is also used in the familiar expression of faith Allahu akbar, meaning God is greatest, or very great, or greater than all. (The -u ending of ?akbaru is silent when final, and the glottal stop ? is often not transcribed.)
Many languages don't have distinct -er and -est forms: for example in French only the definite article distinguishes the comparative and superlative: plus grand que 'bigger than' versus le plus grand 'the biggest'. But I wouldn't call these elatives, because they're not used intensively. In contrast, the closely related Italian has the same system (più grande 'bigger', il più grande 'biggest'), but it also keeps an inherited Latin superlative as an elative form: fortissimo can mean 'loudest' or 'very loud'.