As both @HDMIGuy and @Strega said, you need a content provider to authenticate the ESPN app. Sling TV is the cheapest ($35/month), but if you go that route, make sure you pick the Orange plan ($35/month). The Blue plan doesn't include ESPN, but rather, has Fox Sports. For both ESPN and Fox Sports with Sling TV, you need the Orange+Blue plan ($50/month). Or, Vidgo ($55/month), Fubo ($65/month), YouTube TV ($65/month), Hulu+Live TV ($70/month*), DirecTV Stream ($70/month).
* = Hulu+Live TV is currently $65/month, but price increased to $70/month on December 21.
DBDukes Roku Community Streaming Expert Note: I am not a Roku employee.
If this post solves your problem please help others find this answer and click "Accept as Solution."