PHPMyAdmin 4.0.5 - Grid edit, checkbox, Edit, Copy and Delete features are not available
To fix this, pick a suitable column(s) in your table and create a unique index on it (or on them). Version 4.0 added this verification to avoid other problems when not the intended row is modified or deleted.
See http://en.wikipedia.org/wiki/Unique_key.
[EDIT] However, version 4.5.0 contains an improvement in this regard, see https://github.com/phpmyadmin/phpmyadmin/issues/11061
You should be able to assign a primary key to the table. Just click on the 'Structure' tab when viewing the table you are trying to edit, choose a field you want to be the primary key and there is a button to assign it as the primary key in one of the columns. Go back to the browse tab and you should now be able to edit the table.