While on the face of it a pound of feathers would seem to weigh the same as a pound of gold, this overlooks the fact that gold is universally weighed using a different definition of 'pound' than that used for most other materials.

Precious metals such as gold are measured in troy weight. A troy pound is 12 troy ounces, and each troy ounce is 480 grains, making a total of 5760 grains to the pound of gold.

Most materials use pounds and ounces from the avoirdupois system, and such a standard pound is made up of 16 ounces, where each ounce is 437.5 grains, making a total of 7000 grains to the pound of feathers.

All this means that a "pound" of feathers (or bricks, or lead) is heavier than a "pound" of gold.

The question is an old gag, based on the fact that gold is measured in troy ounces, but feathers (like all material other than precious metals and gemstones) are measured in avoirdupois ounces. Because troy weight has 12 ounces to a pound, but avoirdupois weight has 16 ounces to a pound, the trick answer is that a pound of feathers (at 16 ounces) is heavier than a pound of gold (at 12 ounces).

Another user said:

A pound of anything weighs the same as a pound of anything else.

However, feathers as weighed using imperial weight, which puts 16 ounces to the pound. Gold is weighed using troy weights (for precious metals) which has 12 ounces to the pound.

So a pound of feathers weighs more than a pound of gold, since different pounds are spoken of.

Another user said:

A pound of feathers is heavier- because a pound is NOT always a pound. Gold, silver, platinum- and all precious metals are measured in TROY ounces and TROY pounds. A troy pound weighs less than a standard (avoirdupois) pound.