The intuition is simple: ten holdings with an average correlation of 0.8 behave roughly like one and a half independent bets, not ten. A common approximation for N equally weighted positions with average correlation r is effective N = N / (1 + (N - 1) r).
Worked: twelve positions at r = 0.6 gives 12 / (1 + 11 x 0.6) = 12 / 7.6 = 1.6 effective bets. Twelve at r = 0.2 gives 12 / 3.2 = 3.75. Adding a thirteenth correlated name to the first book changes almost nothing about its risk while adding a thirteenth ticker's worth of monitoring.
Use it as a reality check before adding exposure. If the effective number barely moves, the new position is size, not diversification - and should be judged as an increase in concentration-risk rather than a reduction.
Related: concentration-risk, correlation-matrix, diversification, portfolio-volatility