I am a self-taught violinist and need help understanding this sheet music.I know how it sounds thanks to YouTube but I wonder its name and its meaning.
It's what guitar players would call a barré indication, namely putting down the same finger across two strings. With the preceding open string, this is likely in first position, using the index finger. Basically this is done to play those two notes like the next two notes with a rocking bowing action that keeps the lower fingered note "ringing on" in the same style for the bracketed two notes as it does for the next two following notes.
It's not likely an experienced player would choose to do this in any different manner (you could do it in third position if you played the previous note "2" rather than "0", but it would end up with a 3rd finger barré then for the next two notes), so this is likely spelled out for learners.