Pseudoephedrine, also known as Pseudo or Sudo for short, is a chemical compound commonly found in anti-allergy medicines. It is also frequently used as the primary ingredient in the production of methamphetamine, which resulted in its use being heavily regulated by law.
Walter White and Jesse Pinkman originally used the pseudoephedrine method to make their crystal meth, but soon switched to using methylamine when it became obvious that they could not feasibly obtain enough pseudoephedrine to produce the quantities that they needed to.
During their first cook together, Jesse explained to Walt that pseudoephedrine was the key ingredient in the process, and admonished him not to waste it. ("Pilot")
Following Walt's initial refusal to cook a second batch, Jesse had his friend Brandon "Badger" Mayhew obtain supplies of pseudoephedrine, and used it up in an unsuccessful attempt to replicate the purity of Walt's crystal meth. Badger was furious that Jesse had wasted such a large amount of the hard-to-obtain substance, and attempted to physically assault him, forcing Jesse to leave him in the desert. ("Gray Matter")
After Walt made a deal with Tuco Salamanca to supply a large quantity of crystal meth, Jesse pointed out that the difficulty of obtaining pseudoephedrine meant that there was no feasible way that they could make enough to honor the deal. Walt had already taken this into consideration however, and designed a new cooking process based around methylamine. ("A No-Rough-Stuff-Type Deal")
On watching the CCTV footage of Walt and Jesse's break-in, Hank Schrader initially puzzled over why they chose to steal methylamine, before correctly theorizing that they were crystal meth cooks who intended to use it to remove the production bottleneck that pseudoephedrine caused. ("Seven Thirty-Seven")
After the destruction of Gustavo Fring's operation, Jesse suggested to Walt that they temporarily revert to using pseudoephedrine in their cook, as by now the supply of methylamine was also being tightly controlled in response to the popularity of Blue Sky. Walt refused this idea however, and Mike Ehrmantraut was eventually able to solve the problem by extorting Lydia Rodarte-Quayle into supplying them with methylamine. ("Madrigal")
When problems quickly surfaced with Lydia's supply, Mike also suggested going back to pseudoephedrine, although in this case it was less of a genuine suggestion, and more a way of testing Walt's resolve to go through with a train robbery that would require killing both engineers on-board (though the matter was rendered moot when Jesse worked out how they could steal methylamine from the train without alerting anyone). ("Dead Freight")