Some Amtrak stations/trips do have airline style checked luggage(mostly overnight trains), which is why it's mentioned on Amtraks website. For your specific trip you can ignore it as others have said, since Boston doesn't do luggage check and its not needed.

The overheard racks(and racks at the end of each train car) can fit standard airline checked luggage without issue.

If you're leaving out of south station or New York, I'd suggest getting in more like 10-15 min early just to try and get first dibs on a seat since the train often opens up well before it leaves. For other stations getting there 5 min before is fine(and even in NYP and BOS you'll still get on the train, just less choice of seats).