By default block body does not support Drupal token. To parse token in block body you need to install Token filter.
Following are the steps to install and configure Token filter module:
1) download Token filter module and place in “site/all/default” folder.
2) Go to admin-> module and search for “Token filter”. Select “Token filter” and click “Save Configuration” to activate the module.
3) Now go to Configuration -> Content Authoring -> Text formats. You will see the list of all format available on this page, click on configure (in operation column) of “Full HTML” and enable “Replace tokens”. click “Save Configuration” button.
4) Now open the Admin -> Structure -> block and open any block and place token in body and select text format as “Full HTML” and save it. Now you will experience tokens are getting parse.
You can see a list of token here : https://www.drupal.org/node/390482