A cultural movement is a specific change in society, or more properly, society's attitudes and interests in relation to items of culture, such as art, learning, science, music, etc.
It is more correct to describe the Renaissance as a cultural movement than a period of time. For example, 19th century historians may make claims such as The Renaissance started in Italy in 1450 and progressed through Europe by 1485, finishing on the 22nd September 1601 at 4:30 in the afternoon, with a cup of tea and biscuits. This is completely wrong.
It is more correct to say: The Renaissance describes a particular cultural movement, which embodies changes to attitudes to art, literature, theology, and to a lesser extent science. It occurred during the early modern time period, and affected different parts of Europe at different times. Some of the changes brought on by the Renaissance include increased interest in Humanism, interest in ancient Greek learning, changes in attitudes to education (some few of which persisted until the early 20th century), etc.
Although this is still a relatively simplistic view of the Renaissance (and doesn't address the issue of whether the Renaissance of the 15th century and 16th century really happened the way we think it did or not), it is more correct to identify the Renaissance as a cultural movement in this way rather than a time period.