Click the Borders icon to open the Borders toolbar, where you can modify the border of a sheet area or an object.
This object can be the border of a text frame, a graphic or a table. The icon will only be visible if a graphic, table, object or frame has been selected.
When in Calc: To apply a particular type of border to a single cell, position the cursor in the cell, open the Border toolbar and select a border.Whenever you insert graphics or tables, they already have a complete border. To remove that border, select the graphic object or the entire table and click the "no border" icon on the Border toolbar.
When in Writer: Defining Borders for Objects