别 (bié): In this context, this character is a negative imperative, meaning “don't.” It's used to tell someone not to do something. (It can also mean “other” or “to separate,” but its function here is purely as “don't.”)
紧 (jǐn): This character means “tight,” “tense,” or “close.” Imagine a tight knot or a clenched fist—that is the feeling of `jǐn`.
张 (zhāng): This character means “to stretch” or “to open up.” Think of stretching a rubber band or a bowstring until it's taut.
When you combine 紧 (jǐn - tight) and 张 (zhāng - stretched), you get `紧张 (jǐnzhāng)`, a vivid word picture for the feeling of being “tense,” “strained,” or “nervous.” It's the sensation of being stretched tight like a bowstring. By adding 别 (bié - don't), the phrase `别紧张` literally means “Don't be stretched-tight.”