When you immortalize something, you praise it in a way that's meant to last forever. You could immortalize your favorite pop star, for example, by carving a huge statue of him out of marble.
The existence of Disneyland and Disney World has managed to immortalize the image of Mickey Mouse, especially the silhouette of his ears. Through the years, many artists have chosen to immortalize US presidents through public art like the Lincoln Memorial and Mount Rushmore. The verb immortalize comes from the adjective immortal, or "living forever," with its Latin root, immortalis, "deathless or undying."