This is the 3780th most frequent Russian word.
широко
"Широко" means "widely" or "broadly" in English.
In this sentence, 'широко' means 'widely' and describes the extent to which the window was opened.
Он широко открыл окно, чтобы впустить свежий воздух.
He opened the window widely to let in fresh air.
Here, 'широко' indicates 'widely' in the sense of being known by a wide audience or group of people.
Эта концепция широко известна среди учёных.
This concept is widely known among scientists.
In this context, 'широко' is used to mean 'broadly,' describing the manner of the smile.