Weightlifting shoes, sometimes erroneously called “squat shoes,” are shoes designed for the sport of Olympic weightlifting. They feature a hard, elevated heel, velcro straps, and a tight toe box.
Weightlifting shoes exist because the goal of Olympic weightlifting is to lift as much weight as possible. The sport requires some pretty extreme positions (such as an ass-to-grass overhead squat), and the elevated heel facilitates stronger deep-squat positions while assisting the athlete with stabilization.
These types of shoes have bled into other strength sports, and are sometimes recommended for recreational lifters or competitive powerlifters. A good question to determine whether you need shoes designed for Olympic weightlifting is:
Are you an Olympic weightlifter?
If you answered no, then you probably do not need weightlifting shoes. If you are competitive powerlifter, the elevated heel may make attaining competition depth (hip crease below the top of the knee) a bit easier; that’s because a raised heel reduces the amount of dorsiflexion required at any given point in the squat, making it easier for the knee to travel past the toes so the athlete can sit into a full squat. However, powerlifting doesn’t require much ankle mobility, so simple stretches may be more beneficial - and certainly more cost-effective -than purchasing a $200 pair of shoes.
Advocates of weightlifting shoes might tell you that you should get them for “stability.” This is nonsense. Here’s powerlifter Chris Duffin squatting 805lbs in bare feet:
And here’s world record holder Dennis Cornelius squatting 795lbs in bare feet:
Do you think these lifters are having trouble with “stability”? Of course not. Your feet are stable, and a stable base is indeed a skill unto itself that can be learned - one which weightlifting shoes might actually inhibit in novice lifters. This doesn’t mean you need to squat in bare feet (although doing so can be a great tool for developing even pressure through the foot). You ought to avoid shoes with a soft insole (like running shoes) when lifting heavy weights, but any flat, firm, comfortable shoe will do just fine.