Attribute set is basically a collection of various attributes that are grouped by their relevance. One attribute set can be mapped to a category and subsequently all the products under that product family by default inherit the attributes within that attribute set. for e.g. you are a multi-category retailer and sell Beauty products as well as Fashion Apparel.
For beauty product family, the attributes you will need will be - shade, tone, skin type - there could be some more nuances even within the beauty family. For example - for nail - the attributes required would be different from product for face makeup. So you can setup Attribute Sets specific for Beauty - Face Makeup, Beauty - Nails and similarly you can setup Attribute set for Fashion Apparel grouping different attributes like - occasion, season, style, dress, color, etc.
Attribute sets can also have groups purely from the perspective of grouping the attribute for logical purposes only. To create a new attribute set, follow the steps below:
- Go to Products > Custom Attribute Sets
- Click on New Attribute Set
- Give a name of the Attribute Set
- Add a new group by giving it a name
- Now you can move the specific attributes to a particular group
- Click on Submit
A typical attribute set would look like this 
And a typical group within attribute set would look like this:
