IDW algorithm says that it makes a grid and assigns value to each point in grid depending on the distance of separation. From this definition, it looks like the output is set of equally spaced points. However, the next step, formation of raster grid is not explained. How does the algorithm assign a unique value to a cell/rectangle from equally spaced points. Are the grid points located at center of cells and then the value at point assigned to cell?
yes, IDW is usually implemented so that the value of each cell(pixel) is assigned based on the location of the center of this cell(pixel). Raster storage is just an efficient way to store those equally spaced points, but one should keep in mind that it is a "point center" representation in this case, not an "area-based" representation. Note that this is a one step process: the IDW values are computed only for the cell (pixel) center position and stored in a raster. This is because it is not necessary to compute IDW for positions that are not stored, but in theory IDW values could be computed anywhere in the spatial domain of the observation, so not necessarily on a regular grid.
A consequence of the use of this raster model for IDW is that it will only return the exact value of a point if the point is located at the center of the pixel. (IDW is an exact interpolator, which means in geostatistics that it returns the exact value of an input point at the location of this point).