It's normal. It's a common thing in photography.
The sensor is what's causing it.
Essentially, all camera sensors are made from one slab, the center is the highest quality and goes into a Full-Frame DSLR Camera such as the EOS 1D and 5D MKII. The next ring goes to Semi-Professional APS-C DSLRs as the EOS 70D. Next ring goes to the mid-range DSLRs as the EOS 600D. Fourth ring goes to low-range DSLRs as the 1000D and the better Compact Camera's. Next one to the cheap compact cams. The remnants are used in tiny Smartphone 1/3.2 sensors.
A full-frame sensor is 35mm. APS-C is 16.7mm, and the one in a smartphone is 3.2mm. The bigger the sensor, the better the detail and lesser the noise.
As such, the sensor in a smartphone is the lowest quality available in digital photography.
Now, the ISO setting determines the amount of noise. ISO decides how sensitive to light the sensor is. ISO 100 has the least noise, and every step increases it. On a APS-C in semi-professional DSLR's, this means you start seeing grain on 3200 ISO. In a smartphone, the sensor is so tiny you get grain at 100 already.
There's nothing you can do about it entirely, the best is to keep the ISO at the lowest setting possible at all times. (This increases the time the shutter needs to stay open, so in low light this might mean you get a shutter speed of 8 seconds or more. Keep that in mind.)
There's nothing wrong with your phone, it's just that the sensor in these devices is just made from the worst part of a sensor slab.
It might be a bit more comforting to put it this way:
My 1500 euro Canon EOS 70D, with an 1100 euro EF100mm f/2.8L Macro IS USM does this:
(The prices aren't there to boast, they're there to show what kind of camera it is, as I know this is not a photography forum and people here don't know the difference in camera's by name.)
100 ISO (100%, image cropped)
3200 ISO (100%, image cropped)
12800 ISO (100%, image cropped) (Nobody in their sane mind uses this setting. I had no idea my camera even went this high, I absolutely never go above 6400, and even then I never go above 800 unless I have no other alternative, and only above 3200 in the direst of circumstances...)
You can see the grain in the 3200 starting to appear, and in 12800 it's horrible.
Hope that clears it up a bit