Using two different types of weapons in The Secret World is a cornerstone of maximizing your character's potential. Abilities that consume resources are among the most potent abilities in the game, so it's important to ensure that you can make use of them as often as possible. Almost all of the abilities, apart from healing abilities, that build resources in The Secret World do so for two weapons at once. If you do not have two weapons equipped, then the resources that would have been built for another weapon cannot be consumed. Having at least one ability that can consume resources for each of your equipped weapons is a good way to ensure that your character isn't wasting the powerful advantage of being able to attack opponents in two different ways in the same encounter.
It is important to note that while you may have two weapons equipped, you can only benefit from the statistics provided by one weapon at any given time. The most recent ability used by your character determines which of your two weapons' statistics you currently have. Swapping your weapons allows you to manually select which weapon you have equipped, effectively modifying your character's statistics on the fly. Weapons can be swapped by pressing Shift+R (by default).