For more, see Draw Tools, Vertices
To activate: (in Edit Layer mode) Toolbar
Move a line or polygon vertex.
To use:
Select feature whose vertices are to be moved.
Activate Move Vertex tool. Snaps are activated.
Move pointer to vertex to be moved so a larger box appears which indicates the snap is engaged.
Click and hold. Move the pointer (vertex should be attached) to the desired location and release.
Repeat move as needed.