I've seen this symbol in various places, such as 「日々」, 「色々」, and 「人々」. What is it, and how does it affect the meaning and pronunciation of the word?
It's a repetition kanji or "ideographic iteration mark", it means that the kanji just before should be repeated. The pronunciation changes according to the kanji being repeated, but a lot of the time, the second kanji will be pronounced like the first one, but with a dakuten (hi->bi, to->do, ha->ba). It often makes a word mean "more than one of that thing". Here's some examples:
- 日々(ひび）: days, or every day
- 人々(ひとびと): people
- 色々(いろいろ): various
- 散々(さんざん): severe
- 昔々(むかしむかし): a long, long time ago
- 時々(ときどき): occasionally
- 早々(はやばや): very early
According to Wikipedia, it's called an odoriji (踊り字 ) "dancing mark" in Japanese. I've heard the name that Robusto mentions ("kurikaeshi") more often.
As others have said, it just means you repeat the kanji. However, there is at least one case I know of where there can be a difference between using the kanji iteration mark and not using it. 日々 is ひび (also にちにち, but I think that reading is rare) meaning "daily" or "everyday life". 日日 is ひにち and means "the date" or "number of days". The latter is often written 日にち to avoid confusion, though.
It's a character to let the reader know that the kanji preceding it has been repeated.
In terms of pronunciation, it may or may not affect the pronunciation. For "色々", there is no change and is simply "いろいろ". For words like "日々", "人々", and "時々", they are "ひび", "ひとびと", and "ときどき", so the first character's pronunciation was modified with the dakuten (") marker.
There are cases where the dakuten is not applied though like "佐々木" for "ささき" even though the さ could become a ざ.
That's the repetition sign, called kurikaeshi. It means the kanji that precedes it is repeated. It changes the meaning and sometimes the pronunciation. For example, 「人々」in your example means "people" or "everybody" and is pronounced "hito-bito". 「日々」on the other hand has no change in pronunciation (hibi, or less commonly nichinichi) but it means "daily" rather than referring to a single day.