This form allows you to generate random passwords. The randomness comes from atmospheric noise, which for many purposes is better than the pseudo-random number algorithms typically used in computer programs.
The passwords generated by this form are transmitted to your browser securely (via SSL) and are not stored on the RANDOM.ORG server. Nevertheless, the best data security practice is not to let anyone but yourself generate your most important passwords. So, feel free to use these passwords for your wi-fi encryption or for that extra Gmail account, but you shouldn’t use any online service to generate passwords for highly sensitive things, such as your online bank account.