Recently I was asked by one of my clients, why I put exercises in a certain order. I generally work larger muscle groups like legs and back then move to smaller muscles such as arms and abs. The general rule of thumb has been to work larger muscles and movements in the beginning of your workout.
You can work multiple muscles and joints when doing larger movements. For example, when you’re doing bent over rows, you’re hitting many muscles of your back as well as your arms, core, and legs. As opposed to doing bicep curls, which only isolate your arms.
You also have the most energy and strength at the beginning of your workout. For example, I would have my client do heavy squats first. She would have enough energy to successfully complete the set all while working large muscles such as the quads, glutes, and hamstrings. We could then move on to more accessory work of the legs afterwards. You want your muscles to be “fresh” so you can exert energy to complete the big lift. You can then eventually “burn out” those same muscles by doing accessory work like leg extensions or hamstring curls.
This is the general rule, but depending on your goals you may change up the order of your exercises. Sometimes we do accessory work first to fire up and activate those muscles prior to a big lift. It all really depends, but if you are training more functionally or testing your strength, then I would suggest working bigger muscle groups with multi-joint exercises first.