Mat files are a kind of pose - they are in the Pose library of a Poser content folder, which D|S can find, or the Material library, which it can't (it is possible to convert one of the file types found in the Material library to a regular pose, but not the other). Textures are jpg or other image files which are applied to the surfaces of your figure according to the settings in the Mat file. (if you like, the Mat file is a recipe and the jpg files are ingredients.)

So: are you sure you are viewing a Poser content folder when you are trying to apply Claudia? Did the set come fith files in the Pose library (|RuntimelibrariesPose) or in the Materials library (RuntimelibrariesMaterial) - look at the file list from the readme to check. It's also possible the set came with more than one installer/zip and you haven't yet added the contents of both.