If the 95% VaR is $8,000, conditional VaR is the mean of all losses in that worst 5% - perhaps $13,500. It is always larger than VaR, and the gap between them measures the weight of the tail.
That gap is the useful diagnostic. Two books with a $8,000 VaR but CVaRs of $10,000 and $26,000 are not comparably risky: the second is loaded with tail exposure that VaR is structurally blind to. Regulators moved toward expected shortfall for exactly this reason after 2008.
It is also a better sizing input, because it is what you will actually pay in a bad week. Budget capacity against CVaR rather than VaR, and assume the estimate itself is low - it is computed from the same limited sample that failed to contain the last crisis.
Related: value-at-risk, fat-tails, stress-testing, worst-case-loss