A properly fitting shoe should be somewhere between tight and loose. Shoes that are too tight can cut off circulation and cause your feet to go numb, while running shoes that are too loose can cause hot spots and generally feel uncomfortable.
I personally like to have a shoe that fits snug enough where my heel doesn’t lift and I have a thumb width of room in the toes. It’s important not to tie your laces too tight. I personally like to tie them loose enough that I can remove my shoes with a small amount of force without untying the laces.