To modernize is to adjust or improve something, especially in a way that uses new technology. You might modernize your grandmother's kitchen by buying her a microwave and an espresso machine.
When you modernize something, you bring it up to date. You could modernize your office by buying new computers, for example, or modernize your antique car by installing seat belts and a stereo. At the heart of modernize is the adjective modern, "relating to the present time" or "up-to-date." In Shakepeare, the word modern is often used to mean "ordinary," although today there's more of a sense of "the very latest technology."