Most of the time, it appears that the players being "assigned to Williamsport" aren't going anywhere - if they were on the Reading roster, they're still in Reading, just not on the roster. A few days later, they're back on the roster, and somebody else is "assigned to Williamsport." Keeping in mind that the NYPL is not yet active, so nobody is actually in Williamsport.
Also note that most of the players who have been on the "Williamsport shuttle" are pitchers - and parking a pitcher off the roster for a few days doesn't affect much (particularly with starters, of course).
This will all stop in a couple of weeks, when the Williamsport roster will reflect a group of kids who are actually playing baseball in Williamsport (and other NYPL venues). But for now, being "assigned to Williamsport" just means a player isn't suiting up for a couple of games.