What is the difference between 绿 and 青? Do they refer to different shades of green? I know 青 can be used in many more contexts; it can be used to mean 'young' or 'immature'. I find it boggling how 青 can mean blue too. Do the Chinese differentiate between blue and green? Or does 青 mean blue+green?
I am a Chinese and I don't think 青色 is the same as 绿色 or 蓝色. For me, 青色 is more a kind of blue. Personally, blue and 蓝色 also cover different shades of blue color.
There is a very common proverb:
literally it means 青色 comes from blue but better than blue. Or more straightforward, 青色 is extracted from the blue plant(indigo) but is bluer than the plant. The next part is "冰，水为之，而寒于水"(ice comes from water but is colder than water). This proverb often used to describe how students can achieve more than their teachers, or the younger ones can do better eventually. I think that is why 青 occurs in words other than color, like 青春，青涩，青年, to describe a young, inexperienced stage just like the green used in "green hand".
There is a common color name in Chinese, 靛青，which is a kind of dark blue.
For other use of "青" besides color and the implicit meaning of young， I don't know.
First, the color of rainbow should be 红橙黄绿蓝靛紫, NOT 红橙黄绿青蓝紫. The later one is simple wrong however it was wildly spread thanks to one of Mao's poems.
In order to explain 青, we also need to understand 绿 and 蓝.
The definition of 绿 is quite clear: the color of green leaves/grass. It's the 4th of seven colors in rainbow.
蓝 is somehow vague. The original definition of 蓝 is: a kind of plant that has greenish/blueish color and can be used to extract dye (you can tell that by the top component of 蓝, 艹, which means herb). wiki: Persicaria tinctoria. There was a famous poem, quote:
which means: in the spring, the river water is as green as 蓝(the plant). If you interpreted 蓝 as a color then this line would be incompresensible. However it's hard to tell whether the poet was comparing riverwater to the color of the herb itself or the dye that came from the herb. I would guess it's the herb. Reasoning will be given after next quote.
Later 蓝 become a color (from the dye). 蓝 mostly refer to skyblue/lightblue/waterblue, which can be equal to the 5th color in a rainbow.
The 6th color is 靛, which is blue/indigo. Note the left part of this character is 青. 青 is somehow like indigo/midnight blue/prussian blue. (It can refer to other greenish colors but I'll cover that later.) There are a lot of evidence, for example: 1) if you google 青花瓷 you'll see the color of the pattern on those vases are blue/indigo. 2) 青布衣 was common clothing of peasants in Ming and Qing dynasty and it was dyed with indigo blue.
translation: 青(indigo dye) was extracted from 蓝(the herb) but the color is better.
So you can see 青 is indeed blue/indigo.
However there are other usage to suggest 青 is used as "green". The most notable would be:
Hills are green for the trees growing on them. So why can 青, an indigo color, also refer to green?
I'll blame 五行 theory for this. In 五行, the five major colors are 赤(red), 白(white), 青, 黄(yellow), 黑(black). As you can see there's no 绿 or 蓝 or whatever other coloes of green/blue/indigo hue. However, 五行 was designed to be a theory of everything, a system to describe all phenomenon in the world. Therefore 青 has to take over the responsibility to cover all greenish/blueish items. Especially, in 五行, 青 is related to 木(woods/trees/herbs, one of the five 五行), so later on people started to use 青 for green color.
Last but not least: what is the color 青 in 青天? is it sky blue? Answer: no. If you google "kuomintang" you'll see the flag of kuomintang government 青天白日 is a white sun in indigo background. 青天 is used to describe government officials that are honest and hands clean, literally "as clear as the sky". So I think 青 in 青天 is a loan character(假借) from 清天.
Conclusion: 青 should be indigo blue especially when referring to daily artifacts that were dyed by indigo. However it can also be used to mean green, especially plants.
And according to http://www.baike.com/wiki/%E4%BA%94%E8%A1%8C%E5%AD%A6%E8%AF%B4,
So 青's original meaning is the color of the East, and the East indicate the wood/tree, so 青 originally is the color of the plants after primary growth, it's green. And the East can indicate the Spring according to 五行, so 青 is the color of Spring, so there's a word "青春", and then has a relevant meaning of "young", such as "青年".
And according to the dictionary, 青 could be used for the color of:
And in general, 青 means dark green, or light blue.
Here's a parlance about rainbow does make sense: "红橙黄绿青蓝紫".
As you see, 青 is between "绿" and "蓝".
青色(cyan) = 绿色(green) + 蓝色(blue)
However though in practice, most Chinese tend to interpret 青色 as 绿色 or less commonly as 蓝色.
What many of the answers above provide are the etymology of 青色. The table below give the technical names of all the different shades of green and blue. I have highlighted the more important ones. For the full list, see here.