By installing Chrome you now have two Internet browsers installed on your tablet (the pre-installed 'Browser' and subsequently installed 'Chrome'). When you are using an app (such as BBC iPlayer) that needs to open a web page the app doesn't know which one to use, hence it is asking whether it should use 'Browser' or 'Chrome' to open the web page. When this happens, you select the internet browser you wish to use, and if you tick the 'Default' box, then the next time the app needs to open a web page it will use the one you've already selected without asking you again.
P.S. in the case of BBC iPlayer you should select 'Browser' as 'Chrome' does not support Adobe Flash Player which is required by the BBC iPlayer web site.
I said you were brilliant yesterday (BBC iplayer sideload) so I can't say it again! But thanks so much, getting there slowly. No doubt there will be more to come - I'm addicted to these (simple) discussions. Thanks again.