It means everyone pays separately.
I tthink it is actually one of a number of unkind national stereotypes.
It was at one time also referred to as "Dutch treat," meaning that when someone "Dutch" invites you to go out to dinner with them, they do _not_ treat you (pay for you).
Some other examples--not commonly used any more--are: "Dutch courage" (alcohol), and "to Dutch-uncle someone" (to scold them).