One standard definition for "vernalization" goes something like this:
Subjection of crops (seeds, bulbs or young plants) to cold temperatures in order to hasten plant development and flowering.
However, this definition implies that vernalization is achieved only through human manipulation. But vernalization also occurs naturally. Therefore, probably a more precise definition of "vernalization" is
The process, natural or artificial, whereby plants are readied for flowering through exposure to cold temperatures.
This definition of "vernalization" overlaps considerably with another entry in my glossary, namely, chilling requirements. A chilling requirement (some call it a "vernalization requirement") can be thought of as a standard that must be met in order for vernalization to occur. By discussing chilling requirements, we can quantify the chance of a plant's flowering in a particular region.
We need to draw a distinction between "vernalization" and "forcing," although, again, there is overlap between the two terms. Both words can mean coaxing plants into blooming earlier in the season than would happen in nature. However, when we say that we are "forcing" forsythia flowers into bloom by cutting them and bringing them inside in February, we're talking about providing plants prematurely and artificially with warmer temperatures, thereby immediately forcing them into bloom. As stated above, vernalizing is, by contrast, all about cold temperatures.
"Vernalization" ultimately derives from the Latin word, ver, which means "spring." In the Northern Hemisphere, I suppose it makes sense to say that vernalized plants have been "springified," but just remember that the process occurs in winter, not in spring.