You don't need to override the block that is automatically provided by Aggregator. Much easier to make your own block using Views.
- Go to Views -> Add a New View
- Show Aggregator Item
- You can uncheck 'create a page' and check 'create a block' if you only want a block.
- Give the block a name and Continue & edit
- Under Fields, add the Aggregator Title and any other fields you want.
If you have multiple feeds, give them categories in the Aggregator settings (admin/config/services/aggregator), and then filter by category ID within the view.