There are several ways to delete data you own in Fusion Tables.
To delete a row, click the trash icon. In classic, it appears to the right of the row. In the new look, click to select the row first.
In classic, comments you make and any comments on data you own will show a "delete" link. Click to delete a comment.
If the deleted table was used to create a view, the view will become empty. If the deleted table was used to create a merged table, the merged table will either be empty or will no longer show data from the deleted table, depending on how the merge was done.