The GI Bill does cover grad school - it's not limited to undergrad. The Post-9/11 GI Bill specifically covers graduate and professional programs, so you can definitely use it for a master's degree. The coverage works the same way it does for undergrad: it pays tuition and fees at the school you attend, plus you get a monthly housing allowance while you're studying full-time. The amount you get depends on your tier of benefits and the school's costs, but it's meant to be pretty comprehensive.
One thing to keep in mind is that grad programs can be pricier than undergrad, so depending on where you go, you might hit the benefit cap. That's where you'd need to cover the difference yourself or look into other funding options like loans or employer sponsorship. Also, some schools are better than others about working with GI Bill students, so when you're picking a program, it's worth asking the admissions office directly about their experience processing VA benefits - some places make it way smoother than others.
Your recruiter probably wasn't trying to be unclear, but this is definitely something to verify directly with the VA once you're closer to using the benefits. The rules can shift slightly, and your specific eligibility depends on your service details. The VA website has a pretty solid breakdown, or you can talk to a benefits counselor before you leave service - they can walk you through exactly what your benefits will cover for grad school.