All members can view a grid’s description: simply click on the information action button on the opened grid’s action bar.
All platform members can edit a grid description (even if this is just for private grids within their own private folder area - for user and external member types).
For free accounts, an architect or builder can edit any grid description in the main grid library.
For professional and enterprise accounts, configurable access control will determine who has the access permission to edit a grid's description in the main grid library; see What is configurable access control?
First, ensure you are in edit mode, by clicking the edit mode action button from within the grid action bar. When edit mode is toggled on, click on the information action button from within the grid action bar. You can now update the grid description by clicking inline within the descriptive text area. Changes are automatically saved.