According to engineers at WWDC it's a bug related to iOS 10 Beta 1, should be fixed in the future betas.
Right now you can only install an app once, it will fail if you try to install an app with the same bundle id. A factory reset will let you install the app again or a using a new bundle id will also work until Apple fixes this.
So if you really need to install an update of an app (as the first install will always work) doing a factory reset of the phone or using a new bundle id seems to be the best solution right now.
Update : this seems to be fixed in Beta 2