So an aura, as far as the various Warcraft's and Diablo's have taught us, is a passive buff that emanates from a person and bolsters the abilities of others around them - usually some bolstering of abilities or resistance to some element.
I'll propose that group/raid leaders have unique auras, which provide similar effects to the people they are playing with.
Think about the last group projects or tasks you've done in your life. In most every case, you should be able to identify the group leader's ability to inspire others to either work longer, strive harder, feel better about the task at hand, be more resistant to roadblocks, or be more efficient.
Now - all leaders need to be pushing their groups to have these virtues. It's just natural that some people will excel in some areas more then others. Think about character creation in a game, where you play with slider bars or allot stat points to determine attributes. The sum ability of two equal level characters is equivalent no matter how you spend them, but they can end up looking and feeling radically different.
When a regular group of people changes raid leaders, it feels different. It may be the regular RL is out for the night, has left the game, or your running a semi-pug with another guild. The net result, is things aren't done quite the same, and it can be unsettling.
What I want to establish, is that this is not necessarily the result of weakness. Vene posted not too long ago, "a [raid] is weak if it cannot function without it's strongest link", and I don't want to confuse what I'm saying, with the phenomenon he notes.
When experiencing a change in raid leadership, one must simply adapt to the new strengths brought to the table. If the new leader is as competent ("the same level as") the old one, then they are both going to bring just as much to the raid. If the rest of the group sticks with their same expectations, however, the result will be weakness.
When your group doesn't have Frost Resist Aura, you drop Frost Resist totem, right? Both have advantages, and both have opportunity costs. But if you don't adjust, and keep dropping Healing Stream totem, you're inflicting weakness unnecessarily.
I'll give a rough example of an actual raid leader situation (and examples for this kind of thing is tough, since the really important stuff tend to be more indescribable gut "feeling" types of things). But lets say Raid Leader A's strength comes in the form of whipping the raid through trash at a breakneck speed. When Raid Leader B steps in, who typically coordinates comprehensive boss assignments during trash - the raid ends up screeching to a halt. The entire leadership is tied up with assignments - while the rest of the raid stares at the trash pacing back and forth. Had the differences in their "auras" been noted, people that normally do assignments could have shifted to directing trash - and the raid would go on and benefit from improved assignment coordination, rather then improved trash speed.
My challenge is this - Consider what you/your raid leader's aura is. What do they help groups do, that you find noticeably absent in groups without them/PuGs? How can identifying this help the raid shift its efforts when not under that person's command?