I'm a roleplayer, so learning background information about druid lore and visualizing what my character's life might have been life is useful to me. But for any player, whether you roleplay or not, it can help you get a more immersive feeling out of your game if you can really imagine yourself in your character's skin,... or fur, as the case may be.
So, if you were a druid in Azeroth, what would your life be like? The one certainty would be that a strong connection to nature would have been your primary concern from a very young age, whether as a night elf or as a tauren, but your path to becoming a druid would have been very different depending on which race you were, with great changes coming to you and your people in the very recent past.
Night Elf druids
Since night elves were immortal up until just 6 years ago, as a night elf druid you may be many thousands of years old, though if you were, you would most likely be male. So long ago, there was a strong gender segregation among night elves -- priestesses and sentinels were invariably female, and druids were always male. As a male druid, therefore, you may have studied alongside Malfurion Stormrage, the greatest druid ever known, and learned directly from the demigod Cenarius himself, the fountain of all druidic knowledge in Azeroth. You might have fought alongside them in the War of the Ancients against the first demons of the Burning Legion who tried to destroy Azeroth. You might have witnessed the creation of the first World Tree, Nordrassil, at the top of Mount Hyjal above the magical and dangerous Well of Eternity, and lain in sleep for many centuries while in service to the great dragon Ysera in the Emerald Dream, as she helped guard this Well from the return of the Burning Legion.
It would have been a rude awakening indeed to find yourself recalled from the Emerald Dream to fight the Burning Legion once again in the Third War. But since that war was completed, you would have found your customs, traditions and way of life turned head over heels. Not only was Nordrassil destroyed and your immortality lost, but you would find your connection with the Emerald Dream difficult to restablish, your beloved archdruid Malfurion Stormrage mysteriously trapped inside the Emerald Dream, and leaving the controversial Fandral Staghelm to lead in his place. Cenarius, too, has been murdered, leaving the leadership of druids and night elven society in greater chaos than ever since the War of the Ancients, the corruption of Queen Azshara and the departure of the Highborne elves. And to top it all off, now women are allowed to become druids too!
For one so very old, having gone through so much, it would seem that everything is indeed falling apart. You may side with Staghelm in his attempt to regain immortality through the creation of the second World Tree, Teldrassil with the hope of regaining some measure of what you have lost, or you may side with those who believe that a new age has come and put aside the old traditions in favor of establishing new ones, better suited for the era you now live in.
As a female night elf, your studies of the druidism would have started just a few years ago, and yet with night elf society in such a state of chaos and upheaval, you may rise to great mastery and high rank in just a short period of time, as Arch Druid Renferal has done with the Druids of the Grove in Alterac Valley. You are likely to be very young for a night elf (perhaps 300 years old or so) and eager to work continue the work of uniting druids against the threats that really matter, not to vainly attempt to regain lost glory and immortality.
Previously, all night elf druids were organized according to the totem they studied under, and practiced slightly different variants of druidic magic. They were Druids of the Claw, with a bear totem, Druids of the Talon, with a storm crow totem, or even Druids of the Antler or the Fang. Since the Third War, however these different groups have been united into one, called Druids of the Wild, which studies all druidic magic. Male druids may have strong connections and loyalties to their old totem, while female druids would be likely to have a broader approach.
Tauren have never been immortal, living between 100 or 150 years, but their records, displayed in the tent of the tauren Archdruid Hamuul Runetotem in Thunder Bluff tell a story of their strong connection to Cenarius and his teachings. These tauren myths state that Cenarius came to the tauren and taught them the ways of the Druid. Over time, however, the tauren focused more on their shamanic tradition and lost their deep connection to druidism.
Hamuul Runetotem was able to renew this connection when, during the Third War, he struck up a friendship with Malfurion Stormrage, learned druidism from him, and brought the tauren into the Cenarion Circle.
If you were a tauren druid, it wouldn't matter if you were male or female. Either way you would be part of a new moovement, almost a religious renewal, to get back to your druidic roots. The complicated traditions of the night elves might seem strange to you if you had any association with them, but you might envy how very seeped they are in the druidic teachings, which you may feel are closer to the Earthmother than those of shamanism. You would not have a sense of what the Emerald Dream or Ysera is like, and with your spiritual link to the Earthmother, you would be much more focused on this-worldly affairs than night elves, who might seem to have their head in the clouds.