"打开看看" mean open or check it. Where do you live? If you living in China? The courier will ask you open before they sent it that in case there not any dangerous things.

The stuff have to know what is in the package in order to avoid some dangerous things . On the other hand , the stuff can tell couriers to be careful with the package by making a note , Fragile, for example. Thus "打开看看" just means open it and let me to have a look .

打开看看 the original type is 请你打开，让我看看。Which means please open it and let me have a look. Hope it helps.

It means show something to people.