Shapefiles support four fundamental datattypesdata types: Point., Polyline, Polygon, and Multipoint. Points are simple {X,Y} features. Polylines are ordered sets of points, and Polygons are the areas encompassed by closed simple lines. Polylines and Polygons can be multi-part to model discontinuous features, like a surface street separated by a highway, or a collection of islands.
In the shapefile model, Points can't be multi-part, but there is a distinct Multipoint type to take that role. The difference has to do with the envelope in the data record needed for Multipoint shapes and the different approach to spatial indexing of point and multipoint objects.
Multipoints are an obscure representation option for most point-ish features, but they can be used to optimize the display of large numbers of points. I had a dataset involving tens of millions of features covering the globe, and I was able to successfully draw a hundred thousand features within a single one degree square with subsecond timing by unioning the points into multipoints to reduce the number of features rendered for each tile.
Note that shapefiles don't support anything like a geometry collection, only permtting the specified shape type or a null shape (zero vertices) within one file, so if both single and multi-part point shapes are required, the single-part points will be stored as degenerate Multipoints (with a point count of one, and an "envelope" with the lower-left and upper-right corners coincident with the point itself).This is less efficient in storage (52 btyes vice 16) and the spatial index is not as efficient, either, so if you'll only have single-part points, you should use the Point datatype.