Eldritch Stones are the blocks that Eldritch Monoliths are built with. Those generated as part of a Monolith are indestructible, but a mining scroll will break them which is a way to get in the monolith. However, the ones that you place (by finding or researching) can be destroyed.
Eldritch Stones can only be obtained by the player through Researching and crafting them, or finding them within Monoliths. In the research, Eldritch Stones are classified as Eldrich Knowledge, meaning you must obtain the theory by researching Eldritch Artifacts, followed by researching the resulting Eldritch Fragments.
The researched Eldritch Stone is crafted in increments of four and can be found in chests inside monoliths. It currently has no known uses aside from being a building material. For more information regarding Eldritch Stones and Monoliths, see the Eldritch Monolith page on the official Thaumcraft website.