Intentional dreaming is dreaming with a purpose or intent.
Generally, the intent is stated out loud before sleep, or written into the dream journal before retiring. Once sleep has overtaken you, the intention plays out in your dreams.
The possibilities for examples of these intentions are pretty broad:
You may dream with the intention of remembering your dreams.
You may dream with the intention of experiencing lucid dreaming or dream walking.
You may dream with the intention of communicating with a spirit being.
You may dream with the intention of sorting out or furthering your understanding of something that is not becoming clear to you in waking thought.
You may dream with the intention of fulfilling a sexual fantasy in dream space.
Many people use the term intentional dreaming as a synonym for lucid dreaming, but one need not dream lucidly to dream intentionally.
I have heard the term intentional dreaming used to describe goal-setting and long-term planning toward your “dreams” for the future or the “big picture” for your life. The term is used metaphorically here, rather than literally as I’ve presented it above.