You see it all the time. The jacked dude with massive shoulders, jacked biceps, and pecs that could crush a walnut between them.
But then has absolutely zero legs. Just little chicken legs sticking out from his shorts. Beyond that being sad and a testament to his ability to push himself beyond his comfort zone, it'll have long term effects on his health with less lean mass to keep his resting metabolic rate high, less stability for when he's older and a fall risk, and definitely not helpful in doing much of anything besides curling.
Here are the basic movements of the legs: Push, Pull, Lunge. Each of these types of movements should be incorporated into your leg day. If you're working with a strength coach or a personal trainer, and some of these aren't done in at least every session, then you might want to find a new personal trainer -- perhaps me, whom I'd consider a top personal trainer in Nashville ;-)
PUSH LEG MOVEMENTS
Think of these as anything that is a squat movement. There are goblet squats, barbell back squats, front squats, zercher squats, lateral squats, split squats, rear foot elevated split squat, heel elevated squats.
These movements can be more quad dominant, but hit every muscle group of the leg.
These movements are considered a push, because it's from a static standing position to squat then "pushing" through your legs up and out of the squat to a standing position.
Having a good looking squat is indicative to a lot of other joints working well. Your ankles move well, your knees move unobstructed, your hips have good external and internal rotation, and you've got core strength to keep yourself upright throughout the movement.
PULL LEG MOVEMENTS
Think of these as anything that looks like a deadlift. These are deadlifts, romanian deadlifts (RDL), kickstand RDLs, single leg deadlift, kettlebell swing.
These moves are more hamstring and glute dominant, but hit every muscle group of the leg. Having a strong leg pull helps build strength in your posterior chain (ie, the muscles you can't see in the mirror).
They're considered a pull because the move look like you're pulling something from the floor, the weight is in your hands rather than resting on your back (or body somewhere). If you were take a still picture mid-deadlift, it could look like the person was rowing or pulling the weight weight with their arms.
Deadlifting reveals whether you have good hip mobility, good femur external rotation, a strong upper back, and strong abs/low back to maintain static position the whole time. Properly executed deadlifts should really hit the hamstrings and glutes, but they will also hit the quads.
LUNGE LEG MOVEMENTS
Think of these as anything that is a stepping motion in which the knee bends a considerable amount. These could be forward lunges, reverse lunge, lateral lunges, curtsy lunge, eight point lunges, box step ups, box step downs, stairs.
These moves work the entire leg, but if done properly will hit the glutes more than anything.
I'm not sure where the term "lunge" comes from, I was tempted to call them steps, because a lunge is essentially a massive step that requires the leg to load the knee and hip of the forward leg.
Lunges reveal a lot about your legs as well. First of all, balance: for 1/3 of the movement, you're on one foot. This works your feet, ankle, calf, and hip stability muscles. Lunges will also reveal weakness in your leg muscles -- if you're weak in a certain area, the lunge will look wobbly or disjointed driving out of the hole.
You can lunge in lots of different directions too to hit different parts of your legs. A lateral lunge hits the outside glute and inner groin. A curtsy lunge hits the glute and calf stabilization muscles. Reverse lunge makes the quad work a little more to absorb force going backwards.
Leg day is vital, you can't skip it and should probably work some sort of leg in at every training session. Leg day isn't just doing leg extensions or clam shells on a machine.
To see how your leg muscles stack up, try doing 3 sets of 10 walking lunges and 10 body weight squats. Even for a really in shape person, this will get the heart going and blood pumping. For a couch potato, you'll be wrecked the next day.