The Romans used a less formal script, known as Roman cursive for daily life, while the Latin script we know now was more formal. How did the Latin script displace Roman cursive as a daily form of writing?
Could anyone expand on Roman cursive?
To be very brief, the Latin script we know and use now is based on renaissance "recreations" of ancient Roman writing, which they found by looking at ancient manuscripts they were recovering from monastic libraries, as well as stone carvings. Consider the names for scripts like "Italic" and "(Times) New Roman." They used these scripts to replace the barbaric medieval scripts that were current in 14th and 15th century manuscripts.
Unfortunately for them, the scripts they thought were ancient were actually 9th and 10th century manuscripts written in scripts like Caroline minuscule. This script also developed out of a desire to bring uniformity to the many different types of scripts throughout Europe in the 7th century. These scripts differed so much from each other that it was often hard for someone from one monastery to even read the writing from another. These are the scripts that had descended from earlier cursives and other ancient script styles. If you want more information, any introduction to paleography (for example, the one by Bernhard Bischoff) will go into much more detail and illustrate it with examples.