The Phonology of Standard Chinese by San Duanmu (端木三) has an entire chapter devoted to this topic (The Word Length Problem):
In this section I review six previous approaches to the disyllabic phenomenon in Chinese. For convenience, I call them (a) the homophone-avoidance approach, (b) the speech-tempo approach, (c) the grammatical approach, (d) the rhythm approach, (e) the morphologization approach, and (f) the stress-length approach. These approaches are not all proposed by different people. For example, Guo (1938) suggests that both (a) and (b) play a role, Lü (1963) suggests that both (b) and (c) play a role, and N. Li (1990) suggests that both (c) and (d) play a role. I argue that none of the approaches, nor combinations of them, can explain the disyllabic facts adequately.
In my own readings, I found that the homophone-avoidance approach (which @user58955 explained in his first point) to be the most common explanation. It feels true too because phonological changes since Old Chinese have merged the pronunciation of many words that were once distinct, and modern Chinese languages that have been more phonologically conservative tend to retain more monosyllabicity (such as Min and Cantonese). The book points out several issues with the homophone-avoidance explanation though:
...as Lü (1963) points out, most increase in disyllabic words took place in the past 100 years or so, during which period there has been little change in the phonology of Chinese.
However, this objection could be partially explained by the rapid incorporation of modern concepts (which @user58955 explained in his second point).
There is another interesting point concerning the homophone-avoidance approach:
... many proponents of homophone-avoidance ... assume that classical Chinese mostly consisted of monosyllabic words. However, when Chinese characters were created ... Chinese already had numerous homophones. ... In other words, there must have been many homophones from the beginning. This raises the question of why people did not create disyllabic words to avoid ambiguity then. The answer, as suggested by Guo (1938), must be that classical written texts did not reflect the spoken language, in part because of the scarcity of writing materials, and in part because characters offer more distinctions than speech. ... In any case, there is no clear evidence that classical spoken Chinese mostly consisted of monosyllabic words.
Anyway, the chapter is an interesting read. The conclusion eventually states:
I have also argued that, unlike a popular belief, homophone-avoidance does not play a clear role in the increase of disyllabic words in Chinese. Instead, the increase is mainly due to an increase in new words...
Finally, I have argued that word lengths are constrained by metrical structure, in that some positions prefer a disyllabic words and other prefer a monosyllabic word. ...