Welcome to Android Central! Does this happen on both wi-fi and mobile data?
Try going to Settings>Apps>All, select Google Play Store, and Clear Cache/Clear Data, then Force Stop. Do the same for Download Manager. Now try again.
Even then, Play (the site, not the app) has a maximum number of apps it will download to one user at a time, the rest of them will be pending until a download has finished. So if you try to update a dozen apps at a time, there will be a lot of pending ones for a while. (I'm not sue, but I think the maximum number at one time is 2.)