Pension schemes and insurers owe defined cash flows decades out. The present value of those payments moves with interest rates, so a portfolio that ignores rates can be fully funded one year and in deficit the next without any change in the assets themselves.
LDI hedges that by holding long-dated bonds and interest-rate-swaps whose value moves in step with the liabilities. If liabilities have a duration of 20 and assets a duration of 6, a 1% fall in rates raises liabilities by about 20% and assets by only 6%, opening a 14% funding gap.
Because swaps and repo are used to get duration without tying up all the capital, LDI books carry collateral calls. A rapid rise in yields can force selling to meet those calls, which is how a hedging strategy can become a source of forced liquidation.
Related: dv01, variation-margin