The short answer to this question: absolutely nothing. While BJJ gi belt colors carry some serious significance - primarily in alerting you to the level of shark you're swimming with on the mat - jiu jitsu gi colors don't carry any special significance.
However, while we're on the topic, it's worth noting the history of the jiu jitsu gi colors, as well as when certain colors are more appropriate than others.
First and foremost, white is the most traditional uniform color for many martial arts with Japanese roots. In Japanese culture, the color white signifies "purity" or "truth", which is likely why it was adopted as the color for martial arts training, particularly judo and jiu jitsu. When judo competitions became popularized, a blue gi was utilized to distinguish one competitor from another, and this was subsequently adopted by jiu jitsu.
Today, white and blue are the only colors available for judo gis (the sale of which is heavily regulated by the International Judo Federation (IJF), which keeps regulation judo gis limited to those two colors). The International Brazilian Jiu Jitsu Federation (IBJJF), the largest worldwide jiu jitsu promotion, allows for black gis as well... which is great for those who fancy themselves as modern-day ninjas. However, for the major events, like the IBJJF World Championships, black belt competitors can only wear a white or blue gi in the finals.
The greater jiu jitsu community is quite a bit more relaxed when it comes to gi colors. While some academies have strict "white gi only" requirements during class, most academies don't... which is why you'll see jiu jitsu practitioners rocking everything from grey and green, to camo, pink and everything in between. I've even seen a tie-dyed rainbow gi!
Often, the choice to wear a colored gi over the traditional white gi is simply due to personal preference. However, keep in mind that a white gi is always harder to keep clean - and white - than a colored gi. Even if you take all necessary precautions, your academy may use puzzle mats, which have a tendency to discolor a white gi, or it just may not keep the mats clean enough to eat off of.
Whatever gi color you choose, just remember to tap early and tap often.
Train on... Oss.