A Muhaddith is one who studies and memorizes ahadith, and internalizes the science of hadith–the science that allows us to dissect and analyze ahadith and sort the authentic from the un-authentic. (You can read more about ahadith and their statuses here.) This includes memorizing the biographies of people involved in the narration, including their strengths and weaknesses (in terms of memory and piety).
Shaykh Muhammad Nasir-ud-Deen al-Albani, one of the greatest scholars of recent times, also studied ahadith and became a muhaddith–one the likes of we have not seen in centuries. This is why many contemporaries–scholars, imams, teachers–often will quote a hadith as saheeh or da’eef and say “according to Shaykh Al-Albani”. May Allah forgive his sins and accept all the amazing work he completed during his lifetime, ameen!
You can find a brief sketch of his life here, if you would like more details.