Quick explanation of unity movement via transform manipulation.

unity_movement.txt

code in question:
transform.position += transform.right * Input.GetAxis(axisName) * speed * Time.DeltaTime;
 
transform.position
  position vector of the entity this script is attached to
  
transform.right
  vector representing "right" relative to this entity's rotation. normally is <1,0,0>.  for example, 
  you have no rotation and are facing forward.  your "right" would be <1,0,0>.  if you turn 180 
  degrees, your "right" would be <-1,0,0>.
  
Input.GetAxis(axisName)
  gets value between -1 and 1 for the axisName in question ("Horizontal" or "Vertical").  axisNames 
  are changable in Unity Input Settings.  For keyboards, it's usually 0 or 1 or -1.  You can get 
  "half keystrokes" via Input.GetRawAxis(axisName).
  
speed
  speed is usually a seperate variable because it determines the magnitude of the movement vector.
  
Time.DeltaTime
  amount of time passed between frame updates.  a good way of keeping things framerate independent 
  while still running as fast as user allows.  for physics that need to be deterministic, it's better 
  to use FixedUpdate() instead of Update().
  ref => http://docs.unity3d.com/Documentation/ScriptReference/Time-deltaTime.html

= poem's notes =

transform.position += transform.right * Input.GetAxis(axisName) * speed * Time.DeltaTime;
- can be rewritten as -
transform.translate(Vector3.right * Input.GetAxis(axisName) * speed * Time.DeltaTime);

Translate() will move everything relative to the entities local axes meaning no matter how you are 
rotated, moving "right" will always move you in correct "right" direction.  Vector3.right returns <1,0,0> 
always and is fine here and saves you from hitting transform component to calculate transform.right 
(premature optimization whoo!)
ref => http://docs.unity3d.com/Documentation/ScriptReference/Transform.Translate.html

= examples of move code =
(Western Game)
https://github.com/poemdexter/Western-Shooter/blob/master/Assets/Scripts/Mobs/PlayerMovement.cs
3D Game with WASD movement. Get each axis seperately and then translate it to correct axis 
(x left/right, z forward/back)

(Kids Bop)
https://github.com/poemdexter/2DToolkit-Game/blob/master/Assets/Assets/Scripts/PlayerMovement.cs
2D Game with variable jump height.