What is a Fill and Border property in Adobe XD good for? What are their options and what is a difference between them?

Fill property - allows you to set/remove fill style of the selected shape. It can be either Solid Color fill or Linear or Radial gradient fill. It can be turned on/off by checking/unchecking the checkbox near Fill property in the Property Inspector.

Border - allows you to set/remove border style of the selected shape. The border can have different size, dash and gap, also stroke type (inner/center/outer), cap type (butt/round/projecting) and join type (miter/round/bevel). It can be turned on/off by checking/unchecking the checkbox near Fill property in the Property Inspector.