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The square box with rounded corners and an arrow pointing up? That's for "sharing" or "sending" whatever it is that is currently visible on the phone's display.
For example, if there is an image in Photos, select it, and you'll see the square box with rounded corners and an arrow pointing up. Touch the box with the arrow. You'll see the last several people you've recently texted with and a selection of apps you can use to send the message to someone (AirDrop, Messages, Mail, etc.)
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The arrow icon means that your iPhone is using location services. Shutterstock. When the arrow icon appears in the upper right corner of your iPhone, it means that an app is using location services.