In the example given, typical motion graphics techniques are used. There are several ways to achieve this animation in After Effects. Probably the easiest way is drawing a mask shape per letter on top of the 'logo layer' and keyframe the Mask Shape property. In most cases this is fast to implement and good enough, but in order to achieve a uniform motion I'd recommend to split up the logo into separate letters and use a trim path on a shape layer.
Bring your Shape/Text from Illustrator into After Effects or simply use an After Effects Text Layer (If you don't want to switch between the applications)
Make sure that no layer is selected in your composition and hit G to enable the pen tool
Draw your animation path from the beginning to the end of the shape
Set the contour width of the new created shape layer to a value which covers the shape below
Set the fill color to None by holding Alt and clicking into the color field
If you roll out the shape layer by clicking on the arrow > button left to the layer's name, there should be a appear another > Add Button in Track Mattes column. Click it to add a Trim Paths property
If Trim Paths is assigned to the shape layer go to your last frame, roll out Trim Paths property and click the stop watch of the end value, this should create a keyframe with a value of 100%
Go to your first frame and set the end value to 0% to get something like this:
To use the path animation as matte, set the track matte of the text layer below to Alpha
Note: Consider that the type in the given example is very suitable for this kind of animation.
@Poor is right for the "Ares" text on the left. To the right of that, you've got a single line created with the path tool & drawn on using trim path. The "archive" text has had its position and tracking adjusted using keyframes, and has been masked out to the left of the vertical line.
To take a guess at the fonts used, try using a site like WhatTheFont.