Attributes are kind of an even more general form of families. Families all have to be the same plugin type eg. Sprites - Attributes don't have to be. They are literally an on/off flag - like you can set a bunch of any old objects to "Solid", and then make an event "Bullet collides with solid". Then "Solid" can refer to boxes, sprites, tiled backgrounds, or anything, which it couldn't if it were a family. However, you can't use events to relate to an attribute in general like you can with a family.
You can edit attributes by the 'Edit attributes' link in object properties (at the bottom of the list of checkboxes), or in application properties.
The built-in attributes usually have an effect on various behaviors or plugins. The Platform movement won't fall through 'Solid's, the screen centres on objects with 'Centre view on me', and some plugins like the RTS movement allow you to pathfind around objects of a certain attribute.
And on second thoughts, I think I'll go paste this on the wiki