Kits are one of the perks of having a premium account. Rather than a single Favorites set as with a free account, Kits allow you to save multiple sets of icons to organize your work. For example, if you'd like to save a few icons for a personal project you're working on, you can save them all in one Kit. Then if you have a set of icons you'd like to bookmark for work, you can save those icons within a separate Kit.
When you've found an icon you'd like to place in a Kit, simply click the Save for Later button near the icon. From there you can choose which Kit to save it under or to choose to create a new Kit.
Currently, it is not possible to download all icons saved in a kit with a single click. Each icon will still need to be downloaded individually.