Welcome to the Wefugees Community and thank you for your question.
"Ihnen wurde die Flüchtlingseigenschaft nach § 3 Abs. 1 Asylgesetzes(AsylG) zuerkannt" means that the person addressed in the "Bescheid" by the BAMF is now recognised as refugee (according to the Geneva Refugee Convention) and subsequently will receive a residence permit (by the immigration office/Ausländerbehörde) for three years as well as receive a refugee passport (blue passport). That is good news! Handbook Germany explain the different meanings very well in various languages - please follow the link for more information.
Regarding the sentence "Bei Ihnen wurden Abschiebungsverbote nach § 60 Abs. 5 oder 7 Aufenthaltsgesetz (AufenthG) festgestellt" Handbook Germany write:
If you are not recognised as a person entitled to asylum, a refugee status or subsidiary protection, it will still be examined whether you may stay in Germany for other reasons. In principle, you should not be deported if you are at risk of human rights abuse or may face a serious danger to your life, limb or freedom in your home country (§ 60 (5) or (7) Residence Act). That may be the case, for instance, if you have a serious illness that cannot be treated in your home country. People who have been issued a national ban on deportation will be granted a residence permit which is valid for one year.
I hope this helps and please don't hesitate to get back to us with any further questions.
All the best,