World of Warcraft is based around three roles, Healing, Tanking and Damage dealing (AKA DPS). Most PVE encounters require these roles to be filled to a certain degrees to be successfully completed and designers take this into account when designing them. Each role requires a different skill set and while some principles can apply to many roles going from one to the other can be a hard task for some.
For the longest time ever I have only played one character, a Human Rogue. At some point in Mists of Pandaria however, I decided to try new classes out and level them to cap. I began with the easy classes to level and went for a DK and a Monk. Both of these classes can fill multiple roles plus the shorter queue times for tanks and Healers made it appealing to me. I chose to go Blood for my DK and Mistweaver for my monk. Understanding the mechanics for tanking with the DK came relatively easy to me. Rogues are known for having multiple defensive cool downs and being melee DPS most of the mechanics to avoid with the tank where the same.
The problem came with tank swapping and other tank specific mechanics. Tank swapping seems like a way to keep tanks paying attention on fights where other mechanics are basically irrelevant. It seems like a cop out by Blizzard but it does give some more depth to tanking when it mostly is about positioning and timing cooldowns. It also helped that I have good DK tanks in my guild and other friends who have been tanks for a very long time. As a DPS you are mostly worried about not dying while dealing the most amounts of damage but with tanking the responsibility of not killing everyone adds another dimension of pressure that makes what sometimes seems easy as a hard task. That same pressure can be also translated into healers but to a lesser degree.
When I began healing on my Monk I found it a lot more complicated than tanking. Healers in a group are like a unit, while tanks have their own personal cooldowns to manage, all the healers in the raid have to coordinate theirs. I had some idea of what this was as Smoke Bomb fills that role as well but still does not compare with timing heals. One of the problems I found with healing was trying to not tunnel into the raid frames and die to something stupid. The only time I cared about looking at something that was not my surrounding or raid timers was with getting someone back up on my DK. I always noticed that on certain avoidable mechanics healers where the last to react and never understood why, after playing one I can see that they are constantly looking at their raid frames and sometimes miss out on some mechanics.
If you have never tried playing other classes or roles I encourage you to do it. The responsibility with being a non DPS might feel daunting at first but once you get past it being able to play all the aspects of the game is very fun and rewarding. You might even be helpful to your guild by filling in when someone does not show up or help start other groups for raiding.