Geopolitical History of Simplified Chinese
This is a HUGE topic, which I think is impossible to thoroughly cover in one answer here.

As usual, http://en.wikipedia.org/wiki/Simplified_chinese is a good start.

As for mainland, the simplification efforts and processes are inherently tied to the geopolitical history of the turmoils and revolutions in the first half of the 20th century and PRC, as language is the foundation of culture, which is arguably more true for Chinese than most other languages and cultures in the world. The simplification of Chinese characters symbolizes and exemplifies the goods and bads toward a "modern" China.

Now for the more specific question, I actually cannot think of an example of a word or phrase with very different literal meanings when written in simplified vs. traditional characters. After all it's just the written form that is simplified. However, traditional characters evoke a sense of historical and cultural heritage, so there can be some subtle perceived differences.