Blur whole text and then "unblur" part of it
What you need to do is to use a regular blur effect. You also have to apply the effect to an adjustment layer. I'll explain why later on. Why don't I just make a recipe for you to follow first, and then I'll explain what's going on! :)


  
  Make your text layer and fill it with text.
  Make an Adjustment Layer. (Layer -> New -> Adjustment Layer)
  Make sure the Adjustment Layer is selected, and go Effect -> Blur -> Test some of them (Gaussian Blur is very common.)
  Go to the Effect Controls panel to set the blur to what you want it to be.
  


What is happening now, is that the Adjustment Layer is blurring all the layers below it. So if you have other layers below, you may need to Pre-Compose the two layers so that the Adjustment Layer doesn't affect more than the text layer. And the reason why we are using an Adjustment Layer, is that now we can either animate the layer away to reveal the naked text layer, or we can animate a mask to do the same thing. If you use a mask, you can add a feather that will make it look much better in most cases.

Alternatively, you can make two copies of the text, one with the blur directly on it, and one without any blur at all. Then you could animate the mask of the naked text layer to reveal it, but this is a bit difficult if you are animating the text or something like that, because you'll have to do exactly the same on both layers...

Here I'll explain how to do it with the Adjustment Layer with a mask.


  
  Select the Adjustment Layer and select the Rectangle tool from the top toolbar, and draw a rectangle covering the whole of the text.
  Press M to open the mask settings on the layer. Now you can set the feather to what you want it to be.
  


Move the mask a bit to the right to see how the effect will look like. Remember also that when you are adding feather, you'll have to make the mask bigger because the mask will fade away in the corners...


  
  Animate the mask as you please. Tell me if you want me to explain how to do this! :)
  


If you need to have more layers below the text layer, you need to Pre-Compose it:


  
  Select both the layers, right-click and select Pre-Compose.
  


That's it! Good luck with your movie :)