Last night, Buffalo lost to Montreal, eliminating the Sabres from the playoff picture. Washington beat Tampa Bay, and Ottawa destroyed Toronto. This leaves the Bruins in 7th place. But it isn't really 7th place. The Capitals and Bruins have the same amount of points, but Washington has more wins (the first tie-breaker), so Boston is essentially in 8th place.
The Bruins can clinch a playoff spot with a win against Ottawa AND either Philadelphia losing to New Jersey OR Carolina losing to Florida. If Philadelphia loses and Boston wins, then the Flyers cannot pass the Bruins because the Bruins hold the head-to-head tie-breaker (the 2nd tie-breaker) with Philly.
The Carolina condition is more complicated because of their divisional race. Carolina plays their last game tomorrow night, so if they lose (in regulation or OT), they'll have either 92 or 93 points. That coupled with a Bruins win would mean that Boston would have more points. Therefore, if Washington were to reach 94 points with a win on Saturday, the Capitals would win the Southeast Division, catapulting them up to 3rd place. The Hurricanes would also fall to a position BELOW the Bruins. And with only 9 teams left in the playoff picture, all it will take for the Bruins to get in is an assurance that one of those teams will finish behind them.
If the Bruins win, Philadelphia wins, and Carolina wins; they can still clinch a spot on Saturday. If they beat Buffalo on Saturday, they'd be in. If Washington loses on Saturday, they'd be in. If Philadelphia loses on Sunday, they'd be in.
If the Bruins lose in overtime in Ottawa on Friday, they can till clinch. A Bruins OT loss coupled with a Carolina regulation loss would clinch a playoff spot.
If the Bruins lose in regulation, things get a bit murkier. They would no longer control their own destiny, and would need help from Carolina, Washington, or Philadelphia in order to get in.