Deleting records in ArcGIS10

In order to delete a record, you need to be in "editing" mode:

Highlight your layer of interest

Right click the layer and select "Edit features" then "Start editing"

Now you can open your attribute table, select the records you'd like to delete, right click the records and choose "Delete selected".

When you're done, click the drop down arrow on the editing toolbar and select "Save edits", then "Stop Editing".

Note that the records you have removed have also been removed from its associated files (shp, dbf, etc.).