When a Point, or multiple Points are selected the SELECTION - TOOLS menu will be available. The SELECTION - TOOLS menu contains tools that allow you to edit, change styling, annotate, or perform advanced functions on your selected Points. The menu dynamically adjust the tools available depending on your item selection, with additional tools available when selecting more than 1 Point.

Individual Point selection

Multiple Points selection

Styling group

PointAllows you to change the Point color. 
ShapeAllows you to change the Point shape.
SizeAllows you to change the Point size.

Annotate group

NamePoint item Descriptor & Number displayed over the point in the Viewport.
ElevationPoint item elevation displayed in the Viewport above the point.
LabelAllows you to change the Point item's Label color.
SizeAllows you to change the Point item's Label size.

Edit group

Edit VertexEnables Edit mode for selected Point. Displays the Edit Vertex Mode box where you can select editing options and check X,Y,Z coordinates of the selected Point.

Transform group

To TerrainSelected Point(s) will be draped to the underlying Elevation Terrain by changing their Z value to the same elevation as the Z level of the terrain at their XY location. 
Merge PointsSelected points will be changed into a Multi-Point item. Only visible when multiple points are selected.

Result: Multi-Point