If you push a direction against a wall as you're jumping you can't jump over anything higher than a 2 block wall, but if you're not holding left or right as you're jumping you can get over a 4 block wall. This is true even if you hold down jump the whole time.
There is also a walljump, but it doesn't let you climb up a single wall, so it's not very useful for the level design and is more likely to throw you somewhere you didn't mean to go. The walljump would be more useful if there were vertical pipes that you need to walljump to climb.