Extraverted Intuition is one of the eight function-attitudes defined by Carl Jung.
Intuition (N) is an outlook that focuses on the “filling in” of experience with [mental] “constructs” such as concepts, hypotheses, or theories, which all involve “larger contexts” or meanings behind things and [non-physical] “patterns”. Even physical or visible things, like in comparing one thing to something separate, but has some sort of inferred similarity. Focusing on a property to compare, like its shape; they have turned into an “idea” (as in "the idea of" things). This is what “could” or “couldn’t” be.
An "extraverted" attitude (e) indicates that this outlook generally draws from the environment; or the outer world of "objects" that the "subject" (individual ego) observes.
So extraverted iNtuition (Ne) can be described as "awareness of hypothetical reality inferred from the environment", where one turns outward to “fill in” experience of objects with mental/ideational constructs such as connections or patterns. Every type does this, but for types who prefer Ne, it will be their main form of information-gathering, rather than intuitive data totally from within (Ni), or sensory "facts" (S). These types will be denoted in the type code by an "N" and a "P"; i.e. "xNxP"; the "P" pointing to iNtuition; as the "Perception" function, as being what is extraverted, or attuned to the environment.
The types holding the function as "dominant" are ENTP and ENFP, while for INTP and INFP, it is "auxiliary". (For SJ types, it is tertiary or inferior, and may also develop at some point in life).
An extraverted iNtuition preference will be marked by particular attention paid to emergent patterns and ideas inferred from the objects themselves, like lifting meaning from one context, and applying it to another.