What is accessibility feature in Android? I've seen a setting named Accessibility in my Android 5.0 and 4.2.1. I don't understand what it is and how can it be helpful to me? I would like to know what does it do? 

I noticed that there are options like Greenify and Tasker present inside it. Why are they listed in such setting?

There is more about it that bugs me. I rarely use Tasker on my devices but it works well on 4.2.1. However, I noticed that on CM12 you cannot run a profile using Application context, unless you enable some kind of Tasker's accessibility service. I also found this question related but it is unanswered.

Why is it that Tasker needs this accessibility service in 5.0 but not in 4.2.1? More so, how do I run Tasker with app context in 5.0 without enabling the said service, just like on 4.2.1. I seem to see some lags, though not very drastic compared to this question.
Accessibility is a category of features which are usually used to assist people who are in some way disabled. For example people who cannot see well can turn on Magnification Gesture to triple tap the screen and it will zoom in on whatever screen you are on. Also it can reverse the dark and light colors to help them see and read text better. Also, there are voice options which will read the text on the screen, or flash the Camera flash when the phone rings for people who are hard of hearing. Another common option is one that will read wherever your finger is touching, so you touch a button, it reads it aloud and then if you actually want to click it you would double click right there, which is another option for the seeing impaired.

Tasker has the ability to create certain tasks just like this, which trigger an action when certain circumstance occurs like receiving a phone call, or touching a certain area of the screen. This is why Tasker can be turned on and off from within the Accessibility Settings.

After looking at the actual code for Accessibility Settings in a couple ROMs, including my Team (VanirAOSP) and also CM, I do not see any code to add the package's class into Accessibility Settings, but every ROM usually uses res/xml/accessibility_settings.xml for the Accessibility Settings preference, so I imagine that the Tasker developers are adding the Shortcut Setting into the app themselves now... it is not a CM thing. They must have just started doing it recently, or the Android API just started allowing apps to add to the Accessibility Settings in Android 5.0. I'm not sure which.

So, if it is not something you like then you would probably have to take it up with the developers. I hope that helps you understand Accessibility Settings better and why there is a Tasker setting within it.

Here is the actual change, from AOSP, which occurred on April 11, 2014 which constructs a list of accessibility services to add into Accessibility Settings: https://android.googlesource.com/platform/packages/apps/Settings/+/b4b3082