There are varying opinions on this topic, but I say you should definitely stretch between your workout sets. Let’s see what’s the number one reason for stretching as you work out, what more it has to offer and one petty disadvantage.
Number one reason for stretching is, very simply: to prevent injury & soreness (or is it 2?). While doing stretches, you help your body flush the lactic acid out of your muscles, a by-product of glycolysis (producing energy for movement). It’s like flushing the toilet after taking a dump, if you don’t — you feel awkward the next time nature calls (analogy for fatigue in muscle, intervening with proper gym sessions) and eventually all the smelly turds pile up until there’s no room for more and you can’t answer nature! (Analogy for injury — can’t work out anymore.)
Another benefit is expanding the range of motion, as you gain muscle, unless you stretch, it will become harder and harder to scratch your back — as if it wasn’t the hardest thing in the first place!
A drawback is that apparently you lose some explosive power, something like 2.5%. Nothing to worry about, the advantages outweigh by a long shot. Explosive power is what influences explosive movements, like benchpresses, pushups, …
A good enough reason to stretch in general, not only when training, is that it freshens you up. Especially in the mornings, when after a long night’s sleep, your muscles are tense and contribute to an overall feeling of fatigue / sleepiness.