That's Google app (formerly known as Google Search).
Google app for Android: The fastest, easiest way to find what you need on the web and on your device.
- Quickly search the web and your phone or tablet
- Use your voice to search and more
- Get personalised results based on your location
(Click image to enlarge; image modified but originally taken from Play Store)
As for how to disable it, see How to disable Google Search? -- usually, it is Settings → Apps → All apps→ Google (or Google Search) → Disable.
While I was able to disable this app in my CyanogenOS 12, there is an answer here which contradicts with my statement. Perhaps, it is still valid for some specific scenarios. I recommend a look at it.
To remove it, see Rooted Phone but still can't uninstall Apps.
Also consider https://android.stackexchange.com/questions/86475/nexus-5-stuck-in-boot-loop-after-disabling-google-search.