Consider a large portfolio of many assets. A discrete asset by asset calculation of risk parameters $\mu_i$ expected returns, $\sigma_i^2$ variance of returns and the covariances $\sigma_{ij}$ requires a large number of parameters.
$$(\mu_i)_{i=1}^n \qquad (\sigma_i^2)_{i=1}^n \qquad (\sigma_{ij})_{i \neq j}^{0.5n(n-1)}$$
requires
$$ n + n + \dfrac{1}{2}n(n-1) = \dfrac{1}{2}\bigg( n^2+3n \biggr)$$
parameters. Meanwhile to determine risk parameters under CAPM,
$$(\beta_i)_{i=1}^n \qquad \Big(\text{var}(\varepsilon_i) \Big)_{i=1}^n \qquad r_o, \; \mu_m, \; \sigma_m^2$$
requires
$$ n + n + 3 = 2n + 3$$parameters. So we achieve a large scale dimensional reduction by using the CAPM. In reality we also suffer a small loss in accuracy in order to benefit from a much smaller number of parameters to estimate.