Why is there a half note and quarter notes that use the same stem? How to play it on a violin? and What's it called? Thank you.
You've tagged the question 'violin'. So I guess this is violin music.
Think of the mechanics of a violin, the way the strings are supported by the curved top of the bridge. Mostly, the player wants to bow just one string without touching the others, the curvature enables this. He can bow two strings at once if he wishes. But not three.
This notation asks for the common gesture where the lower notes are played briefly and left to ring, the upper note is then played normally.
(For the sake of completeness, I should mention that fully bowed triple stops CAN be achieved in certain circumstances.)
Why is there a half note and quarter notes that use the same stem?
The composer wants you to come as close as possible to playing three notes at the same time.
What's it called?
It is called a "chord" because there are more than two notes. Two notes played simultaneously would be called a "double stop".
How to play it on a violin?
The two quarter notes are A and E which conveniently you can play as the two adjacent open strings. The half note is a C which you would play as a third finger in third position on the E string so that at the end you can put down your first finger on the E to play the slurred A.
To play this you would start with your bow on both the A and E strings playing the A and the E as a double stop, then put your third finger down so you are playing the A and the C as a double stop, then adjust the angle of the bow slightly to come off the A string and complete on just the C on the E string.