General meaning of the Arabic word Hadeeth or Hadees means statement, news, report, narration or talk.
'Hadeeth' literally means a saying or conversation, as in the following Qur'aanic ayah: “Then let them produce a statement like it, if they should be truthful.” [Surah At-Tur 52:34]
“And when the Prophet spoke (Hadeeth) secretly to one of his wives.”[Surah At-Tahrim 66:3]
Islamic Terminology, Hadeeth is synonymous with Sunnah, though the word ‘Hadeeth’ is generally used to refer to only the sayings of the Prophet Muhammed . The Hadeeth have been recorded by the Companions and collected in the books of Hadeeth. The word Ahadith or Ahadees is the plural of the word Hadith or Hadees.
A Hadeeth consists of two main parts: (a) The Sanad and (b) The Matn
The Sanad: Sanad or Isnad, is the chain of narrators that leads to the text of the Hadeeth. The Sanad consists of all those who narrated the text, starting with the last narrator (who records the Hadeeth in his book) and ending with the Prophet. Following is the Sanad of the Hadeeth mentioned before... Al-Bukhari > Musaddad > Yahyaa > Shu’bah > Qataadah > Anas > Prophet Muhammed (sallallahu alaihe wa-sallam)
The Matn: The text of the Hadeeth or what the Prophet actually said or did is called the Matn. In the Hadeeth mentioned before, the Matn is “None of you truly believes until...”
Ahaadeeth are broadly classified into two categories
>> Sahih (Authentic)
>> Daeef (weak)
We Muslims view the Six major Hadith collections as the most important. They are, in order of authenticity:
1. Sahih Bukhari, collected by Imam Bukhari (d. 870), includes 7275 ahadith
2. Sahih Muslim, collected by Muslim b. al-Hajjaj (d. 875), includes 9200 ahadith
3. Sunan al-Sughra, collected by al-Nasa'i (d. 915)
4. Sunan Abu Dawood, collected by Abu Dawood (d. 888)
5. Jami al-Tirmidhi, collected by al-Tirmidhi (d. 892)
6. Sunan ibn Majah, collected by Ibn Majah (d. 887)
The first two, commonly referred to as the Two Sahihs as an indication of their authenticity, contain approximately seven thousand ahadith altogether if repetitions are not counted, according to Ibn Hajar (May Allah have mercy on Him).
First two books are known as Sahih’ain (Two Authentic Books). And first six books are called as Kutubus Sitta. Many of the Muslims refer it as “Sihai Sitta” (Six Authentic Books). However, scholars have identified many daeef ahaadith in last four books of Kutubus Sitta (six books).
Meaning of Muttafaq Alaih or Muttafaqun Alaih hadith is‘agreed upon'. The term is used for such Ahadith which are found in both the collection of Ahadith books of Sahih Al Bukhari and Sahih Al Muslim. Muttafaq Alaih is also called as Sahihain.
Book of Introduction to the Science of Hadith Classification by Shaikh (Dr.) Suhaib Hassan, http://www.ahya.org/amm/modules.php?name=Sections&op=viewarticle&artid=7