Since you are located in the US, it is unlikely that you will ever be able to find out what it means without back-tracing your mare by phone (calling who you bought her from to find out where they got her, then contacting those people, then continuing down the line until you find whoever branded her). Because the US is so screwed up with our branding, there can literally be thousands of ranches across the country with the exact same brand because they are registered with the individual county. I can register a particular brand with my county but someone else could register the exact same brand in another county, then another person could register the exact same brand in another state in their said county.... You can probably see where I'm going with this.
It is entirely possible that the 02 is her birth year... then again it may have just been a marking to track her foaling if she was ever a broodie, or it could be the number of the mare she was out of, or the stud she was by, or it may be a part of the ranch identification. Unless you can find out where she came from, there is no way to know what it might mean.