Hadith Nabawi has a very close relationship and relevant to the Qur'an. Hadith has an important role in the interpretation of the Qur'an reveals the veil of the secrets enclosed in the Qur'an, and parses and clarifies the purpose of Allah swt in the Qur'an, in the form of orders, prohibitions, and other laws.
As we trace the Sunnah / Hadith from the point of view indicating the laws of the Qur'an, either globally or in detail, we have that Sunnah has four functions;
The content of the sunnah itself is in harmony with that which exists in the Qur'an, so in this case the sunnah acts as a pentaukid (reinforcement) against the Qur'an. As the hadiths point to the obligatory prayers, zakat, hajj, do good, and so forth.
Sunnah serves as an explanation (parrot) of the textual intent of the Quran. The position of sunnah as the explanation there are several kinds:
Detailing things that are still global from al quran. Such as all the hadith related to worship and law in the form of the procedure of implementation, terms, time, and condition, because the Qur'an does not explain until the amount of time and pillars of prayer (for example), then sunnahlah will explain it.
Engulfing absolute words in the Qur'an, such as the hadith which states the intent of the word "يد" (hand) in sura Al Maidah verse 38 which means the right hand and cut at the wrist rather than at the elbow.
Mentakhsis the words that am from al quran, such as hadith which clarifies the vague meanings of the word" ظلم "(tyranny) in Surat Al Anam verse 82, with the intention ظلم meaning shirk.
Mentaudhih improper words from the editors of the Qur'an such as the hadith which clarifies the vague meanings of the word "خيطين" (2 black and white threads) in sura Al Baqarah verse 187, then the Prophet said the intent is black night and white day.
The Sunnah speaks of a law not mentioned in the Qur'an. Examples of hadith for this function are so many such hadiths that forbid the gathering of a woman with a sister from her father or mother ie aunt, and so on.
The Sunnah serves to abolish (nasakh) the provisions of the law which has been mentioned in the Qur'an. This section is based on the views of some scholars who allow nasakh kitab with sunnah
References: Book of Manhalul Lathif pages 13-15