So you're watching South Park, and you want to see what it would be like if two of your favorite characters end up in a relationship. As you become more invested in your 'ship, you may start writing fanfiction, drawing fanart, and defending your 'ship against those imagined by other fans.
Shipping Goggles is when a viewer interprets the smallest, most ambiguous canonical evidence in favor of their 'ship of choice. Maybe that glance lasted just a little too long, or that remark in that conversation could be interpreted as innuendo. The 'ship in question can range from one that seems entirely plausible but doesn't yet have clear canon evidence, right up to a Crack Pairing between characters who are bitter enemies, or live in different universes, or whose sexuality or circumstances makes any relationship between them extremely unlikely. Reasons for putting on Shipping Goggles vary; sometimes it's just wishful thinking, sometimes it's to defend the 'ship against other competing 'ships, and sometimes it's just for fun.
Note that this is not necessarily bad, although it can be in some situations. Many shippers would admit to doing this to some extent; in fact, having your own interpretation of Canon is part of the fun of Shipping. However, it can become obnoxious when people try to force their ships on others.