The eight local parliaments have to agree to an international treaty. Therefore, every European treaty (such as the Treaty of Lisbon) have to pass not only through the Belgian federal parliament, but also to every parliaments of the Belgium’s regions and communities: Flanders, Wallonia, Brussels, etc. according to the Belgian Constitution.
As the future deal over United Kingdom leaving the EU could be engraved into a treaty, all EU states would have to give their parliamentary assent… including the eight Belgian parliaments.
There are fears that one or more of Belgian regions could delay a UK-EU agreement, or even stop it entirely.
More recently, the Comprehensive and Economic Trade Agreement (CETA) has been delayed for few weeks because of the blocking from the Wallonia region.
Read more on La Libre.