Factor Analysis
A statistical method that identifies clusters of correlated variables. The Big Five personality traits were discovered through factor analysis of thousands of personality-describing words.
Factor analysis is the statistical technique that gave birth to the Big Five. Here's how it works: researchers collected thousands of words people use to describe personality (friendly, organized, nervous, creative...), then measured how these words correlated with each other.
Words that cluster together form "factors", for example, "organized," "reliable," "disciplined," and "punctual" all correlate highly, forming the Conscientiousness factor. Across dozens of studies and multiple languages, five factors consistently emerge, hence "Big Five."
This is why the Big Five has strong cross-cultural validity, it wasn't invented by a theorist (like MBTI was by Myers and Briggs), it was discovered empirically in the data itself.