While a raiding environment naturally gravitates to an equal contribution between ten or twenty-five people, when the raid is over, those that participated split apart once again. This is alleviated by the presence of a guild, but even within the guild, individual cliques form and preferences are made for certain individuals over others. This is just natural human interaction. There are those that we prefer to be around, and those that we do not.
For newer raiders, or for raiders who have just joined a new guild, this can become a primary source of discomfort. It's hard to feel like you're part of a team when everyone else seems to have much closer bonds with one another. This is natural as well, given that the others may have been raiding together far longer -- but regardless, the sense of 'not belonging' still remains.
The 'raiding buddy' system is something I've seen evolve naturally over time, and it makes a lot of sense to me, from an outside perspective, so I encourage it. Especially for new raiders, this can help them feel more included and valued as part of the team. Raiding buddies are established by openness and communication -- a new tank may form a closer connection with his healer than the other raid members. A mage might end up closer to his focus magic target, just because they come to depend on one another in that small way. The healer may respect the one DPS who dies the least.
There isn't necessarily a set formula for finding a raid buddy. It's almost similar to experiences back in school, when teachers would ask students to exchange information with a classmate, in the event they were absent and needed to make up work. While having a raiding buddy isn't necessarily for convenience foremost, it offers another line of communication to the rest of the guild. In the event you cannot be online or are going to be late for a raid, it's much less of a stretch to imagine texting or IMing your raid buddy to tell the guild.
At the same time, new raiders will feel less alone. It's daunting to find your way into a new guild with no familiar faces, and it can be very difficult to adapt and find a niche, when others have already developed their cliques and groups. Even if it's something simple like running a heroic, or doing the PvP daily, having a raid buddy ensures that at least one person in a large network of guildmates knows you as more than just 'that shaman healer' or 'our third DK DPS.' And that connection is important; it becomes the foundation that determines whether we enjoy our place in a new guild or not, and whether we are comfortable with our new guildmates.