What is this gutter part and how do I keep birds out

Not sure the purpose, but you could replace that "cover" with a tightly fitted leaf guard section cut to fit. I see metal and plastic versions at your local home stores.

Don't see what the confusion is here. When you see this it's almost always to drain a raised edge rooftop or patio or something. You can adjust the cover so there is no hole for the birds to get through. Use screws as you may want to remove it one day for a cleanout. If the pipe draining into it from the deck is significant size, block it with mesh. Bird can't get in, deck still drains, no problem.