Answer:
Hadith is an Arabic word that means 'saying' when said hadith that it means a saying of prophet Muhammad (PBUH). Its plural is Ahadith (that means sayings). Hadith science is the science that deals with study of prophet Muhammad (PBUH) sayings (or Ahadith) regarding their authenticity, ritual worships rules, morals, ...).
Jalal al-Din al-Suyuti describes hadith science as "the science of the principles by which the conditions of both the sanad, the chain of narration, and the matn, the text of the hadith, are known."