Idiosyncratic risk is everything beta does not explain. It is why a stock can fall 30% on a flat index day, and it is the risk that actually ends accounts through single positions.
It falls roughly with the square root of the number of independent positions, so moving from one holding to nine cuts specific risk by about two-thirds if the names are truly unrelated. Beyond about twenty holdings the marginal benefit is small, and for an active trader the attention cost of the twenty-first position usually outweighs it - see position-limit.
The asymmetry deserves attention: idiosyncratic events skew negative for equity holders. Good surprises tend to be repriced over weeks, bad ones arrive in a single gap. That is the argument for a single-name-limit that holds no matter how confident the thesis.
Related: systematic-risk, single-name-limit, gap-risk, diversification