Muharram is so called because it is a sacred (muharram) month and to confirm its sanctity. Allah's words (interpretation of the meaning): " ... so wrong not yourselves therein … " mean do not wrong yourselves in these sacred months, because sin in these months is worse than in other months. It was reported that Ibn 'Abbas said that this phrase referred to all the months, then these four were singled out and made sacred, so that sin in these months is more serious and good deeds bring a greater reward.
Qatadah said concerning this phrase that wrongdoing during the sacred months is more serious and more sinful that wrongdoing at any other time. Wrongdoing at any time is a serious matter, but Allah gives more weight to whichever of His commands He will. Allah has chosen certain ones of His creation. He has chosen from among the angels Messengers and from among mankind Messengers. He chose from among speech the remembrance of Him (dhikr). He chose from among the earth the mosques, from among the months Ramadhan and the sacred months, from among the days Friday and from among the nights Laylatul-Qadr, so venerate that which Allah has told us to venerate. People of understanding and wisdom venerate the things that Allah has told us to venerate. [Summarized from the Tafsir of Ibn Kathir, may Allah have mercy on him. Tafsir of Surah at-Tawbah, ayah 36].