In Arabic, the word hadith means something like “utterance” or “speech.” (It’s one of those words to which no single translation does justice, one for which a whole complex of cultural assumptions needs to be explained.) One common use of the word denotes “reports” or “accounts” about the sayings and behavior (or sunna) of the Prophet Muhammad and his “companions.” These accounts or reports, gathered together by such scholars as al-Bukhari, Muslim, al-Nasa’i, Abu Dawud, al-Tirmidhi, and Ibn Maja, and, among the Shi‘a (drawing on Muhammad and their imams), by al-Kulayni, Ibn Babawayh, and al-Tusi, form a supplement to and a commentary on the Qur”an, and provide the basis for Islamic law.
In Muslim belief, a hadith qudsi or “holy/divine hadith” ranks rather higher, between the Qur‘an itself and an ordinary hadith. It represents extra-canonical revelation, in the words of God but, having been communicated via intermediaries rather than directly, not included in the scriptural text. Here is one of my personal favorites, slightly modified from the translation given by Mahmoud Ayoub in his Islam: Faith and Hiistory:
I am at My servant’s expectation. And I am indeed with him when he makes mention of Me. If he remembers Me secretly in his mind, I will likewise secretly remember him in My mind. But if he makes mention of Me in an assembly, I will make mention of him in an assembly far better than it. If he draws nearer to Me the distance of a hand’s span, I draw nearer to him an arm’s length. And if he draws nearer to Me by an arm’s length, I draw nearer to him by a fathom’s length. If he comes to Me walking, I will come to him running.