The following definition that was shared by someone on Quora is quite good, though a bit academic. Moral fabric is "a metaphor for the flexible but still assured structure of virtue that forms the basis of integrity and holds society together".

To put it simpler, I would define moral fabric as a set of foundational moral principles (common moral ground) that most people in a particular society agree on and recognize as guidelines throughout their daily lives. These principles form a cohesive environment of values, which is referred to a moral fabric.

Here's a blog post with a potentially better definition: https://nomoralfabric.wordpress.com/2012/10/29/the-loss-of-m....