Keith Hennessey offers a readable explanation of underfunded defined benefit pensions and how they compare to defined contribution pensions.
In a defined contribution (DC) pension plan, an employer commits to contributing specific dollar amounts into an employee’s pension account. The employee then makes investment decisions for the funds in his account. The employee has both the upside and downside investment risk: if he invests well, he will have more for retirement. If he invests poorly, he will have less. The employer usually contracts out to a private investment firm (like Fidelity) for the account and investment management.
In a defined benefit (DB) pension plan, an employer commits to pay the employee a specific benefit amount at retirement. The employer owns both the upside and downside investment risk.
There's a lot more at the link, along with an explanation of the three-way political tug-of-war that causes the chronic underfunding of DB pensions.