In Kami-nomi, Kanon (the idol girl) becomes "transparent" several times throughout her Arc. (eps 5 - 7)
- What is the significance of this?
- What does it mean?
- Does it symbolize something?
looper's answer is correct but not quite complete. This answer will be based on the manga, mostly because I don't immediately have access to the anime, but also because I'm not sure how much of this is explained in the anime. Kanon's arc is flags (aka chapters) 7-10 in the manga.
As the other answer points out, Kanon's idol career made her fear failure, which in idol terms is not being seen by enough people to be successful. That is to say, she is afraid of social invisibility. Her fears manifested themselves physically, making her actually invisible, or at least transparent. That's why she disappears primarily when someone isn't paying attention to her, and reappears once someone acknowledges her. However, at the end of her arc, she doesn't stop being transparent until her self-confidence returns, which is the only way she could successfully perform at a large concert without being afraid of failure.
What that answer misses is how she becomes invisible, or at least transparent, since clearly it isn't something a normal person can do. The answer to this is implied in the arc:
This is an ability of especially powerful katetama (駆け魂, above translated as "runaway spirit"). It isn't really symbolism; rather, it's a very real illustration of in-universe mechanics that don't get a full explanation until much later. We get a better understanding of how this works in two future arcs (flags 81-89 and 90-101; feel free to point out if I missed any earlier arcs where something similar occurs):
These are Yui and Hinoki's arcs. In each of the arcs, the kaketama uses its abilities to widen the gap in their hearts. Yui's arc isn't the best parallel, but we do confirm that sufficiently powerful runaway spirits have the ability to somewhat affect their host's physical condition, in this case switching her body with Keima's. In Hinoki's arc, it's also confirmed that the kaketama generally use this power to widen the gap in their host's hearts (in Yui's arc this was a bit ambiguous). In her case, her problem was that the world was too small, and the kaketama worsened this problem by making her body larger, so that the world would seem even smaller to her. That is very similar to Kanon's invisibility problem, except much more powerful because Hinoki's kaketama was rather powerful.
So, a sufficiently powerful runaway spirit, whose host is saddled with some sort of issue, generally has some abilities related to that issue, which can affect things even beyond the host's mental state. These abilities are used to make things worse, widening the gap in their heart. It's a sort of self-preservation mechanism for kaketama. Of course, we already knew from the beginning that the kaketama could affect the host's mental state, but these arcs confirm that they can also have physical effects that would otherwise be impossible without some sort of magic. This is very likely what happened in Kanon's case. It's the only thing that is hinted at in her arc, and no other in-universe mechanic as of flag 200 or so could really explain this in any other way as far as I can tell.
Some people might point out an issue with this theory based on the events of flag 114 (within the "Goddess" arc). However, later events (flag 142) can at least somewhat explain this.
In flag 114 it's revealed that Kanon is actually the host of the goddess Apollo, in the same way that Tenri hosts Diana. Based on Diana's initial conversation with Katsuragi, while the other goddesses should also have hosted kaketama, these were essentially a way of disguising themselves. So one would expect that Kanon's kaketama was rather weak, not strong enough to have effects like this. However, Yui is also hosting a goddess (Mars), and her kaketama was undeniably strong, even stronger than Kanon's, so it seems that Diana may have been at least somewhat wrong about that. Both Mars and Apollo were dormant during each of their hosts' arcs, which might explain why the kaketama were able to become more powerful.
Before Kanon became an idol, she was "socially invisible" - after the Citron broke up, she feared to be alone in front of a large group of people. The effect of being "transparent" expresses her shyness.