Panoramas are created by taking multiple images of a scene by rotating the camera. These images are then laid out side by side and stitched together to form one seamless image of the scene. When taking the pictures it's important to leave some overlap between them so the software can match up similar points.
This diagram should give you an idea.
The HDR technique can be combined with the panorama technique by capturing multiple exposures at each camera position. Then multiple panoramas are stitched together and finally merged into an HDR image.
A spherical panorama is also sometimes known as a 360x180 panorama. It is a panorama that covers the entire scene in every direction from the perspective of the camera. The numbers 360 and 180 come from the degrees of coverage in the resulting image. 360 degrees side to side and 180 degrees top to bottom. Here's an example: