The third party obstruction happens when a player runs between a teammate who has possession of the ball and an opposing player’s path to get to the ball. Basically, you are blocking the opposing player from defending against your teammate.
As you can see in this play, the passer of the ball continued to run into his teammate and got in between the ball and the defender. The foul was called and the free hit was given to the white team:
This is the moment where the obstruction happens:
If you have any doubts, you can take a look at this video by Hockey Zone: