What is meant by a hadith being sahih (authentic)?

In a Nutshell: Sahih hadith is the narration whose isnad (chain) compromises the transmission of a trustworthy (adl) narrator whose retention is accurate (dabit) from another upright transmitter who has an accurate retentive ability until the end of the chain and is neither shadh (irregular) or mu'allal (defective). The Quran requests that we verify information given to us. قال تعالى : {يَا أَيُّهَا الَّذِينَ آمَنُوا إِنْ جَاءَكُمْ فَاسِقٌ بِنَبَإٍ فَتَبَيَّنُوا أَنْ تُصِيبُوا قَوْمًا بِجَهَالَةٍ فَتُصْبِحُوا عَلَى مَا فَعَلْتُمْ نَادِمِينَ } "O you who believe! If a rebellious evil person comes to you with a news, verify it, lest you harm people in ignorance, and afterwards you become regretful to what you have done.” (Qur'an 49:6) This requires we verify news part of which is to take it from trustworthy narrators. This process has not been prescribed in sharia and it does not need to be. The goal is given so this can be determined via a rational criteria that ensures there are no mistakes in narrated information. Hence we are looking for accuracy and competency in taking a report that can’t be achieved unless it is a complete chain and that chain has narrators who don’t contradict higher order reports, i.e., reports which are more authentic. One of the basic requirements for a hadith to be sahih (authentic) is it cannot be a mursal, munqati' or mu'dal hadith. The mursal is what the tabi’een (narrator in the generation after a companion) has narrated about the Prophet (saw) without mentioning the companion. The munqati' hadith is one where a single narrator is missing in one or more places in the isnad. The mu'dal hadith has two or more narrators missing consecutively from one or more places in the isnad. All of these lack continuous isnads which take them out of the sahih category. The ahadith should not be shadh (irregular) which excludes the sahih hadith from the shadh report where a trustworthy narrator goes against the transmissions of narrators who are more reliable than him. It should not be mu'allal (defective) which excludes the sahih ahadith from the mu'allal report which has a defect. The 'illah (defect) consists of a denigratory thing in the hadith, affecting its rejection, such as the chain of a narrator being continuous while a group has transmitted as mawquf i.e., attributed it to a sahabi. By the transmission of an upright narrator excludes the report narrated by a transmitter whose apparent and hidden condition is not known, majhul al-'ayn, or the transmitter is known to be weak, such a hadith is not considered as sahih. By the transmission of a narrator who has accurate retentive ability (dabit) excludes what has been narrated from someone who has memorised a hadith, aware his transmission is negligent and full of mistakes; this report is not considered a sahih hadith. Conclusion All of these conditions should be satisfied in the sahih ahadith. If any one condition is not met then the hadith is not sahih.