We've all been there, a key player (usually a second tank or healer) goes down and it's either get them up or pack it in. Back in the day Shadowmeld provided bears with the ability to drop threat onto one or more of the expendable DPS to allow the opportunity to get a rez off, if that DPS was worth their salt they "tanked" that boss until it was taunted back a moment later. If not losing one DPS to avoid a wipe was a very good trade. I remember doing this a couple times on the first boss in heroic Halls of Lightning back when it was "new" healers always managed to die there by someone getting charged and running laps around them or something. Anyway that doesn't work anymore.
The new trick is to keep an eye on when the boss takes a moment to stop beating on you to cast something. Most bosses do something like this and if timed properly you can get a rez off and be back in bear form before you get whacked again and possibly one shotted in caster form. This is somewhat of a risky maneuver and should not be attempted if there isn't the threat of imminent failure and there aren't any other druids available to do the job. When your butts against the wall and there isn't any other choice the results can be awe inspiring.
For example I was recently tanking Rotface while the second tank herded slimes. All was going well until the second tank got run over by a large slime and chaos ensued. Luckily there was a naughty poo poo less than a second later which provided more than enough time to get a rez off and finish the fight. I've also snuck a rez off while Rotface turned to spray the group which is much more twitchy and time sensitive, but it is doable. Probably my greatest battle rez while tanking was on Saurfang. The second tank went down, we were already short a healer from a mark and had just a little more to go. I got a rez off while he turned to cast blood boil on someone in the raid. It was pretty awesome, but its probably a 50/50 shot between saving the day and getting one shotted.
A battle rez is a very powerful tool in the right situation, so powerful in fact that it is the one and only ability a bear would ever consider leaving the safety of bear form to use. That is a subtle hint to other druids that they should be paying attention to when their battle rez can be useful and not wait for someone else to make the call. The choice often needs to be made in the span of a global cooldown to be effective. I can recall a few incidents where a battle rez that never came could have prevented a wipe. Usually it is a boomkin oblivious to anything besides their next eclipse proc, but that could just be a coincidence.