The spouse and unmarried children( below 21 years of age ) of an H1B visa holder are eligible for an H4 visa. A person on an H4 status is not allowed to work unless and until the person gets a Change of Status from the INS from H4 to H1B status. This means that you also do not get a Social Security Number (SSN).
You can get a Driver's license, open a Bank account, or even go to college. Children on H4 visas do not need a separate visa to attend school.