What the grade beside a hadith tells you.
Scholars graded hadith by the strength of the chain and the soundness of the text:
A report known to be fabricated is not a hadith of the Prophet at all and may not be passed on as one.
In the Forty Hadith you will see Imam an-Nawawi state the source and often the grade himself, for example "related by al-Bukhari and Muslim" or "a hasan hadith related by at-Tirmidhi". On this site those words are shown exactly as he wrote them.