To imbue is to fill up with or become "soaked" in an idea or emotion, as a sponge takes in water. One visit to a sick relative in a hospital might be enough to imbue a child with a lifelong ambition to become a doctor.
You can use imbue in a similar way as "saturate," or "soak through," to describe a filling or absorbing. A "hue" is a color, and it rhymes with imbue. When you're imbued with something, you are, in a way, colored by it. If you imbue a dish sponge with oily orange water from a spaghetti bowl, the color and the oil soak in. To fill people with qualities or emotions is, for example, to imbue them with strength or optimism.