The Raspberry Pi 3B has a maximum HDMI resolution of 1920 x 1080, and should fill the entire screen of HD displays. If you're seeing a black border around the desktop in Raspbian, there is an overscan function that can be turned off to correct this.

Open the command line window, type sudo raspi-config and press enter.

Use the arrow keys or mouse wheel to select 7 Advanced Options, press enter.

Highlight A2 Overscan, press enter.

Use the left-right arrow keys to select No, press enter.

Press enter for Ok.

Use the right arrow to highligh Finish, press enter.

Close the terminal window, and reboot the Raspberry Pi. Your Pi's HDMI output should now fill the entire screen :)