'Let' alone can't be translated in this context but 'Let into' does Let into = Enter to So you can say: I Enter to my tiny little studio

"Let" literally means "allow" here. Now of course you are allowed into your own apartment, but if you think of anyone else, to let or allow them into your apartment means unlocking the door, opening it, perhaps turning the light on, and showing them in. It's the same idea here for yourself.