Everything has an idea behind it, nothing is accidental. The World has its own rules and law, with strict logic, more than people think or want to believe. Endless and senseless of the soulless human being life are unlogical.
This means, that humans have so-called "eternal soul", an undying true-self. However, in the dispute between believers and disbelievers in the soul's immortality, both are right, because of the transitional and relative nature of the World. The truth, as usual, lies somewhere in between.
In general, the human soul is immortal and has it owns characteristic. The true potential of humans are equal among themselves, that's why you can be whoever (or whatever) you want, but you will be whoever you've decided to be.
So, if the soul is immortal, who are the dead?
This depends on where the descendant's soul is now. Usually the living contact with a part of the mind of the dead, something that was left here or near the human's world. So-called spirits are usually these parts of someone's memories, but they can be useful.
Sometimes you can contact the soul of the deceased if he/she wasn't reincarnated. Another way is to find him/ her in your next life.
In folklore and mythology, we can find references to dead people of three kinds: spirits and others, with physical bodies: the undead, who could come out of the grave at night because of hunger, attack people and cause disease and death. The most popular ways to make the dead stay in their graves were penetrating the remains of the deceased with a weapon or other tools like needles, wooden stakes, along with prayers, spells and herbs to tie them forever have a long tradition. Also, the house was spiritually cleaned with plants. Rowan branches are still used as protection from evil supernatural forces.
Also, there are many folk stories about "immortal" or long-living ones, like vampires, mermaids, "demonic" supernatural creatures in the modern culture, who live in a different realm, but close to humans. These long-living creatures are different and usually hostile to humans.
So, why worship ancestors? Your dead relatives are the power of collective minds, that can protect you and help you in your social life. The clan's power means what they can give you, that's why it's important to keep the strength. This is the power of uniting.
You may have nothing with your family, but if you have, this is one of the keys for your spiritual development. Besides, ancestor worship is about the connection with the oldest.