That's likely the
electronic control module (ECM) or a related component housing. Many cars place crucial electronic components under the passenger seat for protection and to keep them away from extreme temperatures under the hood. It's not always easily accessible, and it might be partially or fully covered in sound deadening material.
While it *could* be something else, the ECM location under the passenger seat is a common design choice for many vehicles, including the Oldsmobile Alero. However, without knowing the specific year of the Alero, it's impossible to be 100% certain.
