HDRI stands for High Dynamic Range Images. They are used mainly for highly realistic reflections, although you can use them to light your scenes without actually using lights.

GI stands for Global Illumination. GI spheres are semi- and half-domes of lights that are used to simulate natural light and soft shadows.

Do a forum search and you will find many threads that deal with these two subjects.

That's about as simple as you can get with these very complex subjects. And welcome to your new Bryce addiction!

HTH,

Mike