And one of my favorite kinds! This is a Sempervivum, which are a hardy succulent, not an indoor one. They prefer to be somewhere that is really bright, yet cool. Think, mountain top, as that's where they have evolved.
There are many different ones, most of which are now hybrids and cultivars. This one appears to be Sempervivum tectorum, one of the most common parents for our garden varieties and named ones.