"Slant" refers to a type of DE razor head where the blade is twisted along the long axis of the blade, rather than simply curved. The only slant heads currently in production are manufactured by Merkur, the Merkur Model 37 (HD handled slant) and Model 39 ("Schräg Vorschlaghammer", or "slant sledgehammer", the longer and heavier model).
Slant-head razors are generally viewed as very aggressive shavers and have been produced in a wide variety of designs, including some that are quite different from the current slant-head designs. Some controversy exists as to whether the Slant-head creates a helically twisted blade or not, and whether the method by which the slanted blade cuts hair is more of a "slice" versus a "chop" (as it is with a standard-head DE razor), and whether the "Gillette Slide" (see 0:35 of the video) produces the same slicing results as a slanted head.
When loading a blade into a slant razor, some people feel that the blade should be parallel with the cap, while others align the blade parallel with the slant bar. The first method aligns the blade with a variable blade gap and uniform blade exposure, while the second results in uniform blade gap but variable blade exposure. The question is frequently asked on the forum    .
DunEdinRanger asked Merkur about this, and Anne Rothstein replied that the "blade is to align with the top (head). This is how you load it easily: hold the top upside-down, place the blade over the two nubs and the thread of the top, then place the handle part (also upside-down) over it, and screw together. That way, the blade also aligns automatically with the top." 
A correctly-aligned blade looks like the picture below (courtesy of DunEdinRanger).
- ^http://badgerandblade.com/vb/showthread.php/203633 - Mike H Poll on Slant alignment thread
- ^http://badgerandblade.com/vb/showthread.php/165247 - Question on loading slant bar
- ^http://badgerandblade.com/vb/showthread.php/17662 - On the Slant
- ^http://badgerandblade.com/vb/showthread.php/18255 - On the geometry of the Slant
- ^http://badgerandblade.com/vb/showthread.php/55984 - How to use a slant? Tips and Tricks for best results using a Slant?
- ^http://badgerandblade.com/vb/showthread.php/87841 - DunEdinRanger Slant alignment thread