Hot springs come from fissures (or cracks) in the earths crust which are filled with water. This water once was in close proximity to a hotspot or magma body, and it has boiled up through the fissure to create the hot spring. I'm guessing that because the pressure on the water is so high, when it reaches high temperatures within the crust it can't just become water vapor, and becomes super-heated. Hydrothermal action that makes hot springs also deposits some very interesting minerals, like pyrite and fluorite.
To get to the spring, a short hike is required after parking at a forest service campground and hiking directly up the hill. My favorite time to go is right at sunset, because in the summer and fall the sun sets directly over the river, creating quite the pretty sight. During rafting season they sometimes bring loads of people by to come sit in the springs, so watch out during the day. The campground and parking for the springs is remote and has ample room, and can make a good takeout camp for Gore Canyon, a class IV+/V- whitewater run.
Directions: From Kremmling, head South and cross the Colorado River. At the top of the hill, take a right (west) turn where a wooden sign says "Radium". It is a decent ways on this road, somewhere around 15-20 miles, but a notable feature that your aren't there yet is a paved pass, that means your close! Take a right (north) turn onto CO Hwy 11, at the bottom of a small but steep gulch, and go straight until you arrive at the campsite. Look for the pictured cliffs, the trail splits up, but head to where there are some trees along the bank of the river.