different ways of defining divinity.

[lilphil1989]

Being a Polytheist in a mainly christian/christian influenced society I often find that most people are unaware that not everyone conceives of a god in a way different from that abrahamnic religions.

Yeah, in my experience that's definitely true, any time I've discussed religion or gods with anyone it's always the montheistic model that gets debated/discussed.

But I would say adding more gods just gives you more to prove

It's interesting the reaction I get from people both theist and atheist when I tell them I do not believe that gods necessarily have to be all seeing and all knowing. People with in my particular group commonly think of the Gods as simply beings that are older and wiser then us. But not necessarily perfect or all powerful.

I'm wondering how do people here define the concept of a god?

Well, I think the concept of an absolutely all-powerful god is ridiculous, the old "can god create a stone so heavy he can't lift it himself?" question, whilst perhaps being a little frivolous, demonstrates the silliness of believing in a being with infinite power/wisdom/etc.

As for a definition of god, I don't define gods for myself, because I don't believe in them, and as lrh9 pointed out, have never observed one so it would be pointless for me to try to lay out a definitive definition. Because something could not meet my personal definition but still be a god, if you follow.
I leave the definition to the one claiming the existence of god(s).

I think there are varying levels of Gods. Small Gods who handle more localized affairs and big Gods who take care of things on a higher level.

What do you base this belief on?

How I do know this? Well I don't know this for certain. But it is coherrent with polytheism.

Well, of course. Any multi-god model is consistent with polytheism!