When Jehovah's Witnesses refer to "hope" they refer to the hope created by the Watchtower Bible and Tract Society through its publications, which they claim is based on the Bible.
First, it is their opinion of the Bible's message that is their hope. The hope is based on the opinion (i.e. belief) that humans were originally created "perfect" and would live forever perfect health on a peaceful paradise earth. Their hope is that through their obedience to the leadership of the Watchtower the god of the Bible will restore them to that set of circumstances. They fear death as they believe that death is eternal non-existence. The idea of not having true meaning and purpose with one's limited life causes a great deal of anxiety in a person. The hope the Watchtower extends is a coping mechanism for this anxiety, but it is not a cure.
The first mistake made in the above belief system is that mankind is born imperfect and because of this imperfection deserves to die. All life, from the smallest microbe, to plants, to complex organisms like animals live in perfect cycle of birth, death, and rebirth. In a sense, Jehovah's Witnesses idea of the way human existence should be is like a true that sprouts leaves and then those leaves never die, fall to the ground to fertilize the earth, and then eventually sprout new leaves.
The second mistake made in their belief system is that eternal life has value. Living forever completely undermines the value of life. Something you could do today can wait 10,000 years if you live forever so one's actions have no meaning.
Life only has value if it is lived. You can only live in the present. If your mind is stuck in the past or worrying about the future you are not in the present. Therefore you are not living. Making plans for the future has no meaning if you are not living now. Jehovah's Witnesses hope is based on sacrificing the now for mythological future created by a late 19th century publishing company bases in Brooklyn, New York.
In short, the definition of hope is simply wanting something to happen in the future. Hope can be a distraction from the present and therefor harmful to one's well being and happiness. If you cannot find happiness in your current situation, in the now, you can never be happy.