Typically, no part of your braces will break. However, one way it can happen is from eating hard, crunchy foods. If you eat carrots or apples, for example, first chop them into bite-size pieces, or cook them to make them soft.
Eating such hard foods can bend or snap the arch wire or break brackets off the teeth. For the same reason, it is best not to chew on ice or hard candy. Sticky and chewy candy is also damaging. Gummy bears, caramels and taffy can damage the braces and also damage the teeth that have brackets attached to them.