What is the difference between colloquial and literary readings of characters?
The wikipedia page for Literary and colloquial readings of Chinese characters  gives us a simple overview:

Differing literary and colloquial readings for certain Chinese characters are a common feature of many Chinese varieties, and the reading distinctions for these linguistic doublets often typify a dialect group. Literary readings (文讀; wéndú) are usually used in formal loan words or names, when reading aloud, and in formal settings, while colloquial readings (白讀; báidú) are usually used in everyday vernacular speech.
For example, in Mandarin the character for the word &quot;white&quot; (白) is generally pronounced bái ([pǎi]), but as a name or in certain formal or historical settings it can be pronounced bó ([pwǒ]); this example is particularly well-known due to its effect on the modern pronunciation of the names of the Tang dynasty (618–907) poets Bai Juyi and Li Bai (alternatively, &quot;Bo Juyi&quot; and &quot;Li Bo&quot;).

The section for Mandarin also goes into more details, saying:

Unlike most varieties of Chinese, literary readings in the national language are usually more conservative than colloquial readings. This is because they reflect readings from before Beijing was the capital,2 e.g. from the Ming Dynasty. Most instances where there are different literary and colloquial readings occur with characters that have entering tones. Among those are primarily literary readings that have not been adopted into the Beijing dialect before the Yuan Dynasty.2 Colloquial readings of other regions have also been adopted into the Beijing dialect, a major difference being that literary readings are usually adopted with the colloquial readings. Some differences between the Taiwanese Guoyu and mainland Chinese Putonghua are due to one standard[which?] adopting a colloquial reading for a character while another standard adopts a literary reading.[citation needed]

It also includes:

Examples of literary readings adopted into the Beijing dialect:

which contains:

Chinese character  | Middle Chinese1   | Literary reading  | Colloquial reading
熟  | ʑǐuk入     | ʂu˧˥  | ʂɤʊ˧˥

So it seems that shu2 was once the literary reading while shuo2 used to be the colloquial reading.
Nowadays you'd be more likely to hear shu2 than shuo2 though.
MDBG defines 熟 as:

shú
cooked (of food) / ripe (of fruit) / mature (of seeds) / familiar / skilled / done / also pr. [shou2]

Here shou2 is just a footnote.
The entry for 熟 shu2 in 规范词典 says:

注意 shú是文读, shóu是白读, 一般通用的词语均可用这两种读音。

It does mention that shu2 is the literary reading and shou2 is the colloquial reading and most words can interchange the readings.
The entry for 熟 shou2 in 规范词典 says:

义同“熟(shú)”, 用于口语。

Same meaning as shu2 just used colloquially.