1080P (1920X1080) is only 2MP of resolution. In some phones, it doesn't matter what resolution the camera is taking video at when you shoot a still. In others, it would only produce a still with the same resolution as the video. Check your phone's specifications. If the camera is 8MP and you have it set in the system settings to take the highest resolution still images, an 8MP camera is capable of producing an image that is
3264x2448 pixels (7,990,272 to be exact). If you're shooting a still during a video shoot, you're probably only getting the 2MP resolution.
For example, the images below are a couple at full resolution on an 8MP (Nikon) camera (click on the image to see it in its resident size).
http://www.dailymobile.net/wp-content/uploads/2009/06/nokia-n86-8mp-camera-sample-01.jpg
http://www.dailymobile.net/wp-content/uploads/2009/06/nokia-n86-8mp-camera-sample-03.jpg
Image Size Calculator/Convertor is a handy little picture size calculator. You enter the dimensions in pixels, then choose the output resolution and it will tell you how large the print will be. You will see that at 96dpi (typical LCD or LED Monitor), the image for a 8MP photo will be 34" X 25.5 ". That same image at 1080P would be only 20" X 11.25".