As mentioned by Webster 1913, Encaustic as an art medium involves the application of molten wax infused with pigment. The ancient Egyptians, Greeks, and Romans all experimented with this medium, melting beeswax, then mixing in earth-based pigments to create a colored wax. It was a popular medium with the ancients because it offered a lustrous, protective, and waterproof way to decorate walls, mummies, and terra-cotta. It was quick, since you didn't have to wait for the paint to dry, you just had to let it cool. But the really attractive characteristic of encaustic was that although an encaustic painting was permanent, the painter could take heat to it and revise/rework it whenever s/he wanted -- whether minutes or years later.
To create an encaustic painting, the ancient painter would first make the colored wax, as described above. Armed with a metal pallet similar to a muffin tin, the painter would pour each wax color into a different indentation, and place this pallet over a metal box filled with hot coals to keep the wax molten. Quickly, the painter would smear the hot wax onto the surface with brushes, spatulas (yes, ancient spatulas), and pointed sticks.
Unfortunately for the ancient encaustic painters, the medium eventually fell out of favor, surpassed by tempera, oil, and acrylic paints as encaustic was difficult, expensive, and time consuming. Thousands of years later, however, encaustic gained popularity and media attention as avant-gardists like Jasper Johns played with the medium. I'm sure you've seen John's 1954 encaustic, Flag. Outside the circles of "fine art," encaustic is enjoying a surging popularity with hobbyists and crafters, because it doesn't require the use of any nasty solvents, it can be used to produce a myriad of finishes from roughly textured to glossy, and because the wax's adhesiveness is great for collages.
But these modern encaustic painters don't fuck around! You won't find any muffin tins or hot coals in a modern encaustic studio. Although brushes and spatulas are still used, an increasingly popular method for applying the wax is using an electric iron, exactly like waxing a pair of snow skis! Other tools include blow driers, heat guns, propane torches, Monocoat irons, soldering irons, hot plates, curling irons, and pretty much anything else that has a controllable heat source.
If you'd like to try encaustic for yourself, and I suggest you do, pick up a cheap travel iron, melt some crayons on there, and smear it around on paper. It's fun! Of course, if you do get into it, you should pick up some genuine encaustic wax, either at an art supply place or the Internet. You might even try making your own if you happen to have some spare beeswax and pigments lying around...