Coffers in the literal sense were strongboxes designed to store and protect tangible valuables such as currency, precious metals, jewelry and deeds from theft. Because linens and clothing were considered nearly as valuable as money before the Industrial Revolution, it would not be unusual for those items to be stored away in coffers as well. The fabled treasure chests buried by rogue pirates would also be considered coffers, and were most likely stolen from their owners intact. Many coffers would have been made from heavy woods augmented with metal strapping, along with forged iron locks and reinforced hinges.
In the financial sense, coffers are the tangible and intangible assets available to a government entity or private concern. While these assets may not be literally stored away in ornate wooden trunks for safekeeping, they are often considered to be a surplus "rainy day fund" outside of the normal funding and budget allocations. A city government, for example, may be very reluctant to tap into its coffers to pay for an unexpected expense. In a sense, a government or business's coffers are viewed as reserves for emergency use only, since they will need to be replenished over time.
Sometimes a natural disaster will cause a local government to tap into its own coffers rather than wait for financial assistance from state or federal agencies. It's not necessarily a question of having the funds available, but more of a question over depleting one's own limited coffers when other alternatives are available. Natural disasters, lowered tax bases or general economic difficulties can all cause local governments to tap into their own coffers before assistance becomes available.
Events outside the normal budget of a government can also require a visit to the coffers. Funding for a war or other military action, especially a protracted war with no foreseeable conclusion, may require a country to tap into its reserves or coffers. Candidates seeking election to an office, particularly on the national level, may view donations from supporters as their campaign coffers. When those funds fall below a certain level, the candidate may feel the need to hold a fundraising event to replenish his or her so-called "war chest" or campaign coffers.