Just because you have braces, doesn't mean you can't eat a wide variety of foods! As long as you're careful, and keep a few limitations in mind, you should be able to eat most of the foods you normally do.
Let's talk about what you shouldn't eat!
If you've been wanting to drop a few pounds, the first week wearing braces is just your chance! For the first day or so, stick to soft foods. Avoid tough meats, hard breads, and raw vegetables.
Before long, you'll be able to bite a cucumber again. But you'll need to protect your orthodontic appliances when you eat for as long as you're wearing braces.
Keep in mind also, that chewing on hard things (for example, pens, pencils or fingernails) can damage the braces. Damaged braces will cause treatment to take longer.