To "wear your heart on your sleeve" means to express your emotions freely and openly so that all around you can see. In competitive zero-sum games it may be a liability to exhibit this behaviour particularly where the precipitant may not be obvious to your competitor.
Chess is an example of a perfect information game. In imperfect information games such as poker, it is very important that the player try and hide their emotions as much as possible. Even still, subtle emotional hints may leak out and be noticed by a skilled opponent. These subtle behaviour changes in the game of poker are known as tells.
The above game between Garry Kasparov and Vishy Anand, clearly shows the devastation felt by Kasparov after realising he had missed the strong previous move by Anand. This clip will go down as one of the all-time great examples of "wearing your heart on your sleeve".
In politics, it is best to remember the advice of Margaret Thatcher, ex-Prime Minster of the United Kingdom:
To wear your heart on your sleeve isn't a very good plan; you should wear it inside, where it functions best.
~ Margaret Thatcher