Hardened Glass is a type of block added by Thermal Expansion. It is similar to Glass from vanilla Minecraft, except harder to break and much more explosion resistant. The block is commonly used to craft advanced devices in the mod.
Hardened Lumium Glass is essentially the same thing, except it emits light as bright as Glowstone blocks.
When placed, Hardened Glass can be harvested instantly by dismantling it with a Crescent Hammer or similar. When broken otherwise, the block will not drop itself as an item, unless a tool with the Silk Touch enchantment is used.