Omniscience means knowing absolutely everything past and to come. Believers in the three Abrahamic religions, Judaism, Christianity and Islam, traditionally believe that God is omniscient. This leads to a few logical paradoxes. If God is Omnipotent can god make himself ignorant? If God knew everything that we would do since before we were born, how can we have free will? If God knows all about suffering, why doesn't he prevent it? See Problem of evil.
The early part of the Old Testament suggests a god who is not omniscient. Adam and Eve can hide from God at least for a time  God has to question Adam and Eve to find out that they have done Original sin.  God comes down to have a look and finds out about the Tower of Babel, he didn't know before. 
Here's a list of Bible passages trying to work out, Does God know and see everything?