It is just the way we say things.
"She plays violin." = "She plays the violin." = "The instrument she plays is a violin."
It means that she plays an instrument and the instrument is a violin and she plays it in general. It could be at any time.
"She plays a violin." could also be used to mean she often plays violin. However, it is used more to refer to a particular place and time.
"She plays a violin in the orchestra." = "She plays violin in the orchestra."
You also might be referring to a particular time.
"Last night, she played a violin." Note that there is no hard rule. We could have said "Last night, she played the violin." - without talking about a particular violin.
In slang "She plays a mean violin" = "She plays the violin very well."
Hope this isn't too confusing.