What is the meaning of the Prophet's (PBUH) saying: "Beware of doubtful matters, for whoever guards himself against doubtful matters has indeed acquitted himself (for the sake of) his religion and his honor"? Does it mean doing them or abandoning them entirely? And what are doubtful matters?

The meaning of "whoever avoids doubtful matters, protects his religion and his honor" is that whoever abandons matters that are oscillating between what is permissible (halal) and what is forbidden (haram) has indeed preserved his religion and protected his honor from blame and ill speech. The intent of the hadith is to command the abandonment of these doubtful matters, and the preponderant opinion is that abandoning them is recommended (mandub) and not obligatory (wajib). The types of doubtful matters vary in their proximity or distance from what is forbidden. Doubt may arise from uncertainty about ownership or the mixing of permissible and forbidden elements. And whoever is unsure about these matters and avoids them has done what is most preferable and will be safe in this world and the Hereafter.