There are two main types of private pensions- defined benefit and defined contribution. In DB schemes the benefit is fixed (it may vary with inflation or length of service, but there's a specific formula for defining what you get) whereas a DC scheme is basically a pot of cash which you add to and is invested in whatever fund(s) you chose.
This issue is around DB schemes - if your DC investments include gilts or related investments they will have dropped, but the impact is pretty clear and transparent.
For DB schemes, they use an investment approach called LDI - liability driven investment. What this means in theory is that they either want to match the expected cashflows or they wants the value of the assets and liabilities to move in the same way in response to the same factors like interest rates, inflation, etc.
The first - cashflow matching - is easier to explain so I'll use that. Imagine you're a pension scheme and you've commited to pay Bob £1000 a month, every month, until he dies. You have some money/assets, contributed by Bob's employers, to use to make these payments. But how do you manage the money so there's enough to always pay Bob. One option is to buy government bonds which will pay out £1000 per month in income. That means your cash inflows and outflows are matched.
<yes, this is a simplification, don't come at me for ignoring mortality, inflation etc...I know!>
But a lot of pensions schemes aren't well enough funded to do that. They don't have the money to buy bonds which will pay £1000 to Bob and all his mates. Or maybe they do, but they're under pressure to get a better return on investments as bond returns have been very low. So what do they do?
One strategy is to buy the bond and then immediately enter into a derivative contract to short term sell the bond, with a commitment to buy it back at the end. Think of this as the financial equivalent of taking the bond to the pawn shop...
This then gives them an inflow of cash, which can be used to buy more bonds or to invest in something else which gets a higher return.
Where this goes wrong is that the various contracts that are used don't just rely on trust. If you take your diamond ring to the pawn shop and the value of diamonds collapses overnight then you just don't buy it back. With derivatives this isn't possible - the contracts basically say that if the value of the bond moves, one of the participants has to pay money to reflect the change in value so that they can't default easily and the other party is protected. In this case, the value of the gilt goes down - so the person holding the gilt now has an asset worth less than the pension fund has committed to repay and so the pension fund has to pay in extra money to effectively cover the drop in value.
Problem is...they don't necessarily have the cash to meet these margin calls, as they've either invested it in other assets entirely, or they've gone through several rounds of buy - pawn - buy more - pawn, and so are far more exposed to this movement in prices.
This only covers one way of doing it, there's many others, but they all had the same basic issue - need to meet massive margin calls on derivatives which lost value as gilts collapsed. And as people tried to free up cash by selling assets, the situation spiralled.