"I proclaim the Olympic Games open." Every two years with words similar to these, the Olympic games officially begin. To proclaim is to exclaim or declare.
When you proclaim something, you are saying it loud and clear and in public. A doctor can proclaim you healthy after you have recovered from a long illness. The panel of judges may have trouble proclaiming the winner in a very tight race. What you are saying out loud can be called a proclamation. Proclamations were once only made by Kings or other ruling leaders which is why the word proclaim has an official feeling to it.