These are tree resins, brought up out of Yemen. Amber, fossilized resin, smells sweet when burnt, and so does copal resin, the incense of the tropical Americas.
The trees were scratched to get them to "bleed," and the drying resin scraped off and wadded into small balls. Have you ever seen the blocks of resin used by players of bowed instruments? Just like that. They would then be sent in caravans elsewhere in the world.
When you bought a basket, or a spoonful, of incense, you got a bunch of granules or blobs of amber solid. It burns better if you grind or break it to a coarse texture. You don't want it blowing away as powder on the rising hot air.
So then you make a fire, and get an ember, and set the incense on it. The ember melts and burns the incense grains.
There were organic aromatics used, like what's known today as grains of paradise, and a variety of herbs. There are aromatic woods, like sandalwood and cinnamon. Even the leaves of a cinnamon tree smell like it.
Any scent ingredients can be mixed with fine charcoal in a paste and made up into cones or rolled on sticks, and that's where you get today's incense cones or incense sticks, made with aromatic oils.
And that's how incense is really used, then and today.
You can also derive oils from frankincense and myrrh and wear them on your skin or hair. You can tuck sachets of the grains among your clothes. For parties, the ancient Egyptians put cones of scented wax or fat on their heads (the origin of party hats?) and let them melt sweetly in the heat rising off the partyers.
Majno Guido, in The Healing Hand: Man and Wound in the Ancient World, looked into the reputation of myrrh for wound healing. Topical application is actually of some help keeping down infection, as are honey and garlic.