Politics was defined by Aristotle as the 'Master science': that by which we try to improve our lives. The improvement of one's life is not politics in itself, but that which results from the process is politics. Each individual or group of individuals trying to better their life naturally leads to disagreement, as not everyone is the same.
These disagreeements tend to hover over two main areas: how 'we' should live, and how this should be decided. This social activity can be considered a form of conflict resolution (more a search for the solution than its achievement) through the process of conflict between aspirations, and cooperation as these aspirations are reconciled in order to function together, and not resort to violence and/or disorder. This concept of conflict resolution to make, preserve and amend social rules is however restricted to western style democracies.
Politics can be considered in a broader manner as the 'art of government'. This view stems from the Ancient Greek system of the 'polis': city state. It is concerned with policy making and amending, as the government is 'politics' by responding to pressure from the population, and controlling what David Easton described as the "authoritive allocation of values" - its policy output. Again, however, this view is restricted as it revolves around a system of society that has a (democratic) government.
A more catch-all definition is given by politics being public affairs: all interaction in the public sphere, that is, units in society which are open (in theory) to all members of society; is political and therefore politics. That which is in the 'private' arena, the domestic and cultural sphere, is not politics. This idea has definite pitfalls as it specifies the area in which 'politics' operates, yet does not specify the nature of what politics is.
Politics can be best defined with the introduction of another concept: power. This cynical view of the process see politics as the ability to achieve a desired outcome through whatever means, using scarce resources available. Lenin expressed "Politics is the most concentrated form of economics"(sorry). This definition encompasses all spheres of society from the trade union to the parliament to the community centre and family. Naturally, many elements of the other ideas should be incorporated into this, as due to the very nature of politics, it cannot be contained under a single concept or idea, however in order to consider 'politics' and not 'democracy' or 'government' it is important to consider that politics operates in all spheres of society with many different processes and methods.