Why are climbing shoes bent?
Climbing shoes are bent downwards to enable you to put more weight on very small edges. By being bent downwards, you are able to apply more force on the small edge without the shoe slipping off.
Bent climbing shoes are normally better for bouldering and overhanging routes, as they allow you to have a better grip on the holds, which enables you to pull harder on your toes and keeping your body close to the wall. All of this allows you to reserve more energy in your arms.
Though they are mostly used for bouldering and overhanging routes, they are not limited to them. There are many climbers who prefer aggressive downturned climbing shoes over neutral ones for sport climbing also.
Another element of aggressive climbing shoes is a slight twist in the direction of the big toe. This allows you to put even more force and power onto the toes, allowing you to have an even better stance on those very small edges.