Basically, the idea is that (roughly) until the season begins, if a player's salary cap hit is not in the top 51 salaries for that team, then his salary doesn't count at all against the cap. So, when you release a player in the top 51, you save that player's salary (since he doesn't earn it), but you then immediately add in the salary of the player who then moves into 51st place.
So, for example, when they cut O'Connell, his $385K salary was dropped, and Brandon Tate's $310K salary was added to the cap, for a net savings of $75K (unfortunately, the Pats also had to swallow O'Connell's $314K in signing bonus acceleration, so the net result is a loss of cap room).