If you want to use table attribute item, you can now (QGIS > 2.2) filter the display of features according to the atlas coverage feature, and this will also filter the composer attribute table item during output or atlas preview.
- In the properties menu of your layer, you need rule-based method to style the layer that you want to show the attribute table;
- Set a top rule as
contains( $atlasgeometry, $geometry);
- Add a new style or styles using the + sign, and drag them on top of the first rule.
And you are done, now the atlas output will filter the display of features that are not inside the atlas feature, and the attribute table won't list them either.
This works well if you want to list the attributes of several features in a different layer than the atlas coverage layer.
Note: Your layer will look empty in the QGIS map canvas, but it will work well in atlas output and preview.
Another option is to use labels instead and print the atlas coverage feature attributes using the following expression
'My Field Name: ' || [%myfieldname%].