You've already probably figured out that, in this quotation, Shakespeare is drawing a comparison between someone who is a coward (that is, someone who is afraid to face the challenges of life, such as dealing with difficult situations, taking risks, and fighting for what he or she believe in) and someone who is valiant (that is, someone who is brave in facing the challenges of life, is never afraid to face difficult or risky situations, and will always fight for what he or she believes in).
When you look at just the first part of the quotation, "Cowards die many times before their deaths," try to think of how someone can actually "die many times" before they actually die. Right away, you realize that Shakespeare is using death as a metaphor (because a person can't physically die multiple times in a single lifetime). Here, he uses the metaphor of death to convey how a person feels inside when he or she runs away from a challenge. That person "dies" a little inside each time he or she chickens out, meaning that he or she loses a little strength of character each time he or she refuses to face a challenge of life.
Now take the second part of the quotation, "The valiant never taste of death but once." Shakespeare is saying that a valiant person dies only once, which probably means when he or she actually physically dies. So, Shakespeare isn't using death as a metaphor in this part of the quotation. He is saying that a person who is not afraid to face the challenges of life doesn't "die" inside like the coward does. This person can hold their head up high and be proud that he or she faced that difficult situation or fought for what he or she believed in. So, when this brave and valiant person physically dies, this is the only time he or she will know death because he or she has never been afraid to face the challenges of life.