From BlenderWiki

Vertices Tools

Here we will see mainly some of the options in the Specials/Vertex Specials and Mesh » Vertices menus.

Merging Vertices

This tool allows you to merge all selected vertices in an unique one, deleting all others. You can choose the location of the surviving vertex in the menu this tool pops-up before executing:

At First

Only available in Vertex select mode, it will place the remaining vertex at the location of the first one selected.

At Last

Only available in Vertex select mode, it will place the remaining vertex at the location of the last one selected (the active one).

At Center

Available in all select modes, it will place the remaining vertex at the center of the selection.

At Cursor

Available in all select modes, it will place the remaining vertex at the 3D Cursor.

Collapse

This is a special option, as it might let “alive” more than one vertex. In fact, you will have as much remaining vertices as you had “islands” of selection (i.e. groups of linked selected vertices). The remaining vertices will be positioned at the center of their respective “islands”. It is also available via the Mesh » Edges » Collapse menu option…

Merging vertices of course also deletes some edges and faces. But Blender will do everything it can to preserve edges and faces only partly involved in the reunion.

AutoMerge Editing

The Mesh menu as a related toggle option: AutoMerge Editing. When enabled, as soon as a vertex moves closer to another one than the Limit setting (Mesh Tools panel, see below), they are automatically merged.

Remove Doubles

This is a very useful tool to simplify a mesh – but it is quite basic, if you want something more efficient, have a look to the Decimate modifier.

Basically, it merges the vertices that are enough close of each other. This distance is set in the Limit numeric field of the Mesh Tools panel – note that the value is in Blender Units, and can’t be higher than 1 BU.

Rip

Rip creates a “hole” into a mesh. In fact, it makes a copy of selected vertices and edges, still linked to the neighbor non-selected vertices, so that the new edges are borders of the faces on one side, and the old ones, borders of the faces of the other side of the rip. Hence, it is supposed to be used with only edges and/or vertices selected – as soon as a face is selected (explicitly or implicitly), this tool will fail with message “Can’t perform ripping with faces selected this way”. If your selection includes some edges or vertices that are not “between” two faces (manifold), it will also fail with message “No proper selection or faces include”.

In fact, I think it only works when you select non-crossing edge loops… In general, you should properly select one (piece) of edge loop, as when only individual vertices, or several different edge loops, are selected, the edges that will be split (i.e. orientation of the rip) seem quite unpredictable…

Split

A quite specific tool, it makes a sort of copy of the selection, removing the original data if it is not used by any non-selected element. This means that if you split an edge from a mesh, the original edge will still remain unless it is not linked to anything else. If you split a face, the original face itself will be deleted, but its edges and vertices remain unchanged. And so on.

Note that the “copy” is left exactly at the same position as the original, so you must move it (G) to see it clearly…

Separate

This will separate the selection in another mesh object, as described here.

Smooth

This will apply once the smooth tool.

Make Vertex Parent

This will parent the other selected object(s) to the vertices/edges/faces selected, as described here.

Add Hook

Adds a Hook modifier (using either a new empty, or the current selected object) linked to the selection. Note that even if it appears in the history menu, this action cannot be undone in Edit mode – probably because it involves other objects…

Blend From Shape and Propagate To All Shapes

These are options regarding shape keys.