What are the illustrations they use to show information in Japanese TV called? I don't know if I'm describing them well, so I've included a picture.
Are you referring to this physical board itself? Then there is no well-known specific name for this type of board. It's probably just called ボード or 情報ボード. Handheld smaller boards (roughly the same size as sketchbooks) are commonly called フリップ. See these image search results. Text digitally superimposed on screen is called テロップ.
Or are are you referring to the names of these specific illustrations? I'm at least seeing a 人物の写真, a 人物関係図 and 会話の再現イラスト, but the catch-all term for these illustrations is perhaps just 情報 ("information").