A god is a superhuman being or spirit worshiped as having power over nature and/or human affairs (also known as a deity). They are the central focus of a religion (a system of beliefs and teachings revolving around the belief in and worship of a supernatural being). In some accounts they are also the creator (or creators) of the world, the universe and everything in it - in-universe in the case of some fictional universes. When it comes to the power level of different types of beings, gods are at the top (often with various power levels if there are multiple gods both in fiction and real-life religions).
In real-life there are various religions and the majority of the world's population are religious, and even some non-religious people believe in the existence of a god or gods (theism and deism). The most common religious belief systems are the Abrahamic family of religions (primarily Judaism, Christianity and Islam, with Christianity having the most followers when this was written) which are Monotheistic (belief in a singular God) and share many common elements and root. Evidence of theism goes back well into human prehistory. God or gods are also the origin of the term "miracle"; originally the term for an extraordinary and welcome event that defies, or is inexplicable, by natural or scientific laws and is either proven to be, or attributed to, a divine agency. As a result, divine power trumps any other power in a fictional story (and real-life depending on what one believes), and is the only thing in fantasy that trumps magic.
A person's belief (or lack thereof) in a god is a very significant factor in their worldview and as such often serves as a guiding philosophy. This is because this belief shapes people's views on the big things such as the purpose of life, how life should be lived in relation to oneself and others and what happens to people after they die. On the upside, this often leads to teachings with the goal of unity, peace and co-operation as per the teachings of most religions, some of which are adapted by or also found among non-religious systems. On the downside, this can lead to clashes over how the people involved do the will of whichever god/s they follow or whether or not people should follow a god or religion at all which can involve arguments and factionalizing, or in some cases worse things like pogroms and wars. Since they are an overarching and fairly common element in cultures, they often appear or are referenced in fiction.
There are cases, including in some belief systems, of people or things being mistaken for gods that aren't, or masquerading as gods. Given the inherent authority in godhood, some people use the claim for personal gain, out of extreme arrogance or both.
tl;dr - What the God-Emperor of Mankind aspires to be in authority and eternalness while at the same time alternately despising and fighting or denying the existence of (Note: while the Emperor is deified and worshiped in the Imperium, few if any claim the Emperor made humanity and the universe).