Omniscience, also sometimes known as being all-knowing, refers to Gods ability to know absolutely everything. This characteristic is usually treated as a consequence of one of two ways in which God exists: either because God exists outside of time, or because God exists as part of time.
If God exists outside of time, then Gods knowledge is also timeless this means that God knows the past, present, and future simultaneously. One might imagine that God can directly and simultaneously observe the past, present, and future, and this perception of events is what allows God to know it all. If, however, God exists within time as well, then God knows all of the past and present, through direct perception; knowledge of the future, however, is perhaps dependent upon Gods ability to infer what will happen based upon Gods total knowledge of all factors which lead to the future.
Unfortunately, the most absolute sense of omniscience has been found to be incoherent. If God were truly omniscient in an absolute and unlimited sense, then God could know things which are logically impossible to know. Can God know that 2 + 2 = 5, even though that isnt true? Can God know what decisions God will make in the future? If God exists within time, then such knowledge is logically impossible if God also has free will; because of this, many philosophers and theologians have argued that God can only know that which is logically possible to know.
If omniscience were Gods only attribute, the logical limitations might be sufficient; however, other limitations have been found to be necessary because of other attributes which people tend to assume that God has. Without these extra limitations, the definition of God would become logically contradictory, and it would be reasonable to conclude that God, as defined, cannot exist.
For example, can God know what its like for God to play soccer? Some conceptions of gods in the past allowed for them to be able to play sports, but classic philosophical theism has always postulated a non-material, disembodied divinity. Such a god cannot possibly play soccer an apparent contradiction to omniscience, especially since I am capable of knowing what its like to play soccer. Any direct experiential knowledge of this sort would thus be problematic at best, God can know what its like for others to do these things.
To consider another example, is God capable of knowing suffering? Once again, some theistic systems have imagined gods capable of all manner of suffering and privation; philosophical theism, however, has always imagined a perfect God who is beyond such experiences. It is inconceivable to believers in such a god that it would ever suffer even though humans are obviously quite capable of it.
As a consequence, another common limitation to omniscience which has developed in philosophy and theology is that God can know anything which is compatible with Gods nature. Playing soccer is not compatible with the nature of a non-material being. Suffering is not compatible with the nature of a perfect being. Thus, God may not be able to know how to play soccer or know suffering, but those arent really contradictions with divine omniscience because the definition of omniscience excludes anything contradictory to the nature of the being in question.
If that isnt bad enough, philosophers and theologians have found themselves devising a number of other limitations upon the definition of omniscience in order to allow for many more things which God cannot do while retaining the characteristic of omniscience. For example, it is argued that Gods omniscience doesnt include procedural knowledge (knowing how to do things, like ride a bike) or personal knowledge (knowledge derived from personal experience, like knowing war) only propositional knowledge (knowledge of true facts). This, however, seems to reduce God to a type of computer storage bank: God contains all facts that exist, but nothing more interesting.
A detailed examination of these and other restrictions should be left for another time; what is important to see here is that omniscience has been whittled down bit by bit until there is very little left of the original concept. Arguably, you and I are omniscient under some of these refined conceptions which have become so weak. Any conception of omniscience which could allow us to argue that we are also omniscient has become irrelevant, especially when combined with the observation that we are capable of knowing a great many things well outside the ability of this allegedly omniscient god.