Unfortunately, there isn't one simple answer to what a bro file is because there are no rules, laws, or copyrights regulating the use of file extensions. Consequently, many programs create these files or save data in this format for differing reasons and purposes. There are some common uses for this file extension and common ways to convert one of the appropriate type to a different file format.
Bro files are regularly created by a program called Tree Professional Broadleaf Creator or OnyxTREE Broadleaf depending on the version. This program is a 3D modeler used for creating trees and bushes. The file created can only be opened by the software that creates it, but the software can save its models in a variety of formats making it able to be opened by other software.
Some Roland/Boss digital recording hardware devices record audio tracks in bro file format. Roland offers conversion software called BR Wave Converter which can convert these files into more common audio formats such as .wav or .aiff, or convert common audio file formats into .bro to be usable on their hardware devices. This software can be downloaded from Roland's website.
Embroidery and stitch files created by Bits and Volts software are saved in the this format, and a number of more common computerized embroidery programs can read and convert these files. Broderbund's Create a Booklet/Brochure Project software saves brochures with the extension, too.
Bro, an open-source network intrusion detection system based in Unix, uses the bro extension for internal policy scripts. There is no reason to convert these files because they contain information that is only relevant to this specific software.