There are two meanings for eternity: Either time has no beginning and no end, or there is no time at all. In science, there is neither one nor the other. Here, time is always measurable, thus never infinite, but always finite.
The idea of eternity exists among thinkers, philosophers. In ancient times, people thought the world was infinite, that is, eternal. It was thought to have no beginning and no end.
Eternity exists in many religions, especially where there is only one God. The Jews, the Christians and the Muslims imagine their God as infinite. He has no beginning, so he has always been there. He also has no end, so he is eternal.
Many Christians believe that they will have eternal life after death. But it is not clear whether this life lasts indefinitely or whether there is no time there. The problem here is also that the New Testament was originally written in Greek. From there, the expression that stands for eternity can be translated differently.
Other religions and cultures also know about eternity: in Hinduism, for example, there is the idea that the soul of man comes from infinity and re-enters it after redemption. For Hindus, life is only a kind of "interruption" of eternity.
In our everyday life, by eternity we simply mean a very long time. When we see a doctor in the waiting room, for example, we say, "That takes an eternity". This does not mean that we will never be seen, but only that we have to wait a very long time.