Most hockey color commentators will try to convince us that scoring the first goal of a game is crucial to getting the eventual win. Of course, a team can't win unless they score at least one goal, so they do have a point; but does it have to be the first one?
Compared to other sports, hockey goals are rare, with an average of less than six total goals per game. Goals are also somewhat random with no real pattern in time as to when they are scored. Finally, they are what statisticians call "memoryless," meaning their probability of occurring is not tied to a previous event (like an extra point in football depending first on a touchdown or the number of runs scored from a home run depending on the number of base runners).
Hockey goals are rare? What does that make a goal in soccer?
The way I read it, the author means it in a relative sense. Relative to basketball, where you can net 2-3 points for each basket or football where a touchdown gets you six points and you've got a chance for an extra point or a two-point conversion for a total of 8 points.
I think it gives you a good chance at winning as well, since by scoring the first goal like the poster above me said the other team has to score two in a row, but it also gives your team some more momentum as everyone gets excited for scoring a goal. Also, it may deflate the other teams confidence, especially in a very tight 0-0 game where they were playing very well but finally go down 1-0 in the third or something to that nature