outside a gate; beyond one's expertise
Literally 'outside the gate'; figuratively, refers to something outside one's field of knowledge or experience. Often used in the phrase 門外漢 (もんがいかん) meaning 'layman' or 'outsider'.
Please wait outside the gate.
その話題は私には門外だ。
That topic is outside my area of expertise.
門下 means someone who belongs to a teacher's school, while 門外 means someone outside it or unrelated to the field, so the two are near-opposites despite sharing 門.
Compound of 門 (gate) and 外 (outside). The figurative sense is a natural extension of the literal meaning.