With the Hero's Clothes on, Link can only swim nearly directly upwards (pressing A) and diagonally up (holding control stick without pressing A), and the iron boots (or unpowered Magic Armor) allow for moving downward. This means that he normally can't swim sideways, but with tap swimming, he can.
For swimming horizontally:
Alternatively, for moving a little horizontally while mostly sinking:
Players will often begin sinking into Lake Hylia for Pillar Clip before positioning Link directly above the pillar, so tap swimming a little horizontally while mostly sinking is necessary to position him correctly for the clip. After clipping through the wall, reaching the loading zone for Lakebed requires moving mostly horizontally and a little bit downward, so it is necessary to tap swim horizontally with a toggling rhythm frequent enough to make Link trend downward.
Note the horizontal speed watch on the right side of the screen in this example. Link's maximum horizontal speed is 8 in the diagonal swimming animation and 1.28 while wearing iron boots and sinking. For the sinking portion of the video, tap swimming allows the horizontal speed to reach 8 momentarily on each toggle but mostly stay low while Link sinks; in the horizontal swimming portion of the video, tap swimming keeps the horizontal speed at 8 most of the time but allows Link to descend slightly.