An example of a canon 'shippy' moment between Kim and Ron.
"Shipping" is the concept of two characters within any series being paired together, typically romantically. Kim Possible is no exception, having a wide number of ships supported by it's fans. 
Among the most well know ships within the Kim Possible fandom includes the canon Kim/Ron (K/R) and Drakken/Shego (D/S). There are also several popular non-canon ones such as Kim/Shego (KiGo), Ron/Bonnie (RonBon), and Joss/Wade (Jade). Shipping is often a topic of fanfiction and fanart within the Kim Possible fandom, most of its boards having a thread denoted for either general shipping or specific ships, as a way to limit shipping as a topic to avoid debates due to often high intensity conflicts and ship warring.
Ship Warring:
Ship warring is when fans of one ship begin to bash that of another ship, usually one that is opposed to it or conflicts. Shipping Wars have occured in the Kim Possible fandom, notable ones happening within boards such as RS.net in the past before it was settled and forced to stop by moderator action.
There is a fine difference between ship warring and simply disagreeing. Ship warring is typically in the form of a direct attack on a ship, such as stating that "ship X is stupid". Simply disagreeing or honest debate would be along the lines of "I disagree with ship X due to Y shown in episode Z". The later of which is typically permitted on boards, while the former is often simply flagged as direct flaming.
Popular Ship Overviews:
This is a brief overview of popular ships, including those considered canon.
Kim/Ron (Canon)
Kim and Ron, for the first three seasons of the show, remained nothing more than close friends. Although the ship was toyed with in some smaller moments and feelings were implied, the ship was considered in canon secondary in light of Kim's early crush on Josh Mankey during the first two seasons.
However, in the Season 3 episode Emotion Sickness, the ship was explored via the affects of a device called the 'moodulator' which had Kim agressively pursuing Ron romantically. With the end of the episode having Kim state the moodulator was the only cause, it seemed like the ship would not happen in-canon.
However, at the end of the original series finale, So the Drama, the ship became canon, and remained so into Season 4 when the series was renewed.
Drakken/Shego (Canon)
The relationship between Drakken and Shego is one that had changed rapidly over the course of the show. At first it remained a typical employer-employee relationship but steadily blossomed into something further, though overt shippiness has for the most part been minimal on the show.
The first clue (albiet likely unintentional) that gave this ship credance was in the Season 2 episode Blush, where Drakken commented about a personality quiz asking how they'd show their love to someone being put some form of mind control on them. Drakken had done this to Shego (and Kim) in the Season 1 episode The Twin Factor. The next major clue was, like for Kim and Ron, the Season 3 episode Emotion Sickness, during which Shego was also affected by the moodulator and acted romantically towards Drakken, though it was not brought up later.
The ship was teased properly in Season 4, particularly in the actual series finale Graduation, with Drakken and Shego rushing towards each other when they meet up with each other on the alien ship before awkwardly breaking away. At the end of Graduation, the ship became canon (albiet non-explicitly), and was confirmed as such by Steve Loter afterwards.
Kim/Shego (Non-Canon)
KiGo is considered to be one of if not the most popular ship amongst the Kim Possible fanbase. The pairing is non-canon, and typically runs on what is refered to as 'subtext', or reading between the lines of different scenes to find deeper/hidden meanings. The primary source of subtext for this ship is the interaction between Kim and Shego during their frequent battles. Shego's nicknames for Kim such as 'princess' or 'cupcake' as well as Shego stating in Season 4 that she was to be the only one to defeat Kim are popular sources of fuel for this pairing. The Season 4 episode Stop Team Go also served as fuel, with Kim stating that, when not evil, Shego was like a big sister to her.
Although non-canon, the KiGo ship has sparked conisderable debate and has attracted attack due to being a lesbian pairing, particularly from extremely advocative K/R shippers, and some particularly advocative KiGo shippers had felt free to fire back. These tensions have simmered out of the majority of the fandom, but regardless of this, KiGo remains one of the most controversial and popular ships of the Kim Possible series.
Other Ships:
Joss/Wade (Non-Canon)
This ship is a somewhat fringe one which pairs Kim's cousin Joss Possible with Wade, Kim's mission control. It is non-canon in nature and often refered to as "Jade" for a ship portemandu.
Felix/Zita (Canon)
Felix and Zita were originally characters introduced in different episodes, and did not interact until "Graduation", where they were paired together, though Zita did not have any speaking lines during that episode and the two had never been in the same episode before that point, leaving the dynamic of their relationship unspecified other than that they were together.