LuxRender runs on all recent computers running OS X 10.5 (Leopard) or 10.6 (Snow Leopard). The program does not run on older computers using a G4 or G5 processor or on OSX 10.4 or lower.
The file you just downloaded contains an installer that will install LuxRender. Optionally, it will also install LuxBlend, the exporter for Blender. Please pay careful attention to the instructions in the installer.