Select that big, red Delete button, which brings up a warning asking you to confirm or cancel:
If you're sure that's the asset you want to remove, then you can click this other big, red Delete button and it'll be gone!
The ability to delete assets is only available to those with Uploader permissions or higher.
Deleting Multiple Assets
The simplest way to do this is to Shift+click to select multiple assets at the same time and then repeat the process used for deleting individual assets.
The only difference is that all the notifications will reflect the number of assets you're deleting instead of one specific asset.
You can also use the action menu on any Batch to delete all of the assets it contains, if necessary.