It means that your SSN is link with your EAD, means that when you start working for whatever employer you must show your SSN and EAD. With your EAD you can work whatever kind of work to whoever you want, there is no restriction about it. Employment exceptions can happen like there are some type of jobs that a US citizenship or US permanent residency is required.
The note in your SSN was created since there are cases that the person can have a SSN for other reasons but are not for work. So when the person show the SSN the employer should check for the work authorization from DHS, the EAD that you have.
And yes you can use that SSN to open a bank account, or add yourself in the bank/credit/*bills account of your spouse or other reasons that you need a SSN unless the company (some financial companies) doesn't accept it.
Good luck,