It can be argued that Kant's Critique of Pure Reason is one of the most important works of modern philosophy. It can also be argued that it is one of the most difficult philosophical treatises ever written with scholars still debating exactly what Kant intended to say. To paint a complete picture and accurate picture of Kant's work would near impossible in the form of a blog. But today I intend to outline a brief and accessible description of the background against which the Critique of Pure Reason was written.
Kant remarked famously in his Prolegomena to Any Future Metaphysics (intended to be a more accessible text outlining some of the key points of the critique), that it was David Hume who awoke Kant from his dogmatic slumbers. The dogmatic slumbers of which Kant is talking about is the acceptance of the Leibniz-Wolffian philosophy that was dominant tradition in academic philosophy in Germany at the time. While Kant's pre-critical writings are predominately Leibniz-Wolffian in nature it is apparent that he was never satisfied with the philosophy as such. Leibniz-Wolffian philosophy can be described as a rationalistic philosophy. Rationalism derives all claims to knowledge through the exercise of reason. Leibniz contended that human understanding contains within itself principles that are known to be intuitively and can be used to form the axioms of a complete description of the world derived from reason. Providing a picture of the world as it is, rather than from any particular experiential perspective or point of view.
Conversely the man who awoke Kant from his dogmatic slumbers, David Hume, held a somewhat opposing view. Hume an empiricist denied the possibility of knowledge through reason alone as reason cannot operate without ideas and ideas can only acquired through experience by way of the senses. The content of every thought must be in some ultimate way be derived from experience at least originally. Hume divides all human understanding into categories 'Matters of fact' and 'Relations of ideas'. Matters of fact are essentially empirical propositions that can be known through reference to experience. Knowledge through reason however is limited to consisting in relations between ideas, the truth of the proposition that 'All Unmarried Men are bachelors' derives it's truth from the relations between the ideas contained in the sentence. Other examples of a relation of ideas for Hume are the propositions of geometry and mathematics. Hume has also been taken to be a rather radical skeptic about several issues including the nature of the self, the existence of an external world and what most worried can't about induction and causation. Whether Hume was such a radical skeptic as he is often portrayed is debatable with some reading his works as providing a more naturalistic account (see Galen Strawson).
The problem with Hume's empirical method and skepticism was that it reduced all knowledge about the world to the point of view of an individuals own experience. The skepticism that Hume is often taken as endorsing is clearly intolerable and it is no wonder that it awoke Kant from his dogmatic slumbers. It was through what Kant perceived was wrong with both the philosophies of Leibniz and Hume to the outlook that he adopted in the Critique of Pure Reason. Neither experience or reason alone is sufficient for knowledge, it is only through the synthesis of the two that Knowledge can be obtained. Knowledge obtained through the synthesis of the two is both objective and transcends the point of view of the individual observer making legitimate claims about the external world. There however remains a limit on the knowledge that can be obtained through the synthesis of knowledge, we cannot obtain knowledge of the objective world 'as it is inself' independent of any possible experience or point of view. Kant aims to achieve this with the introduction of the novel concept synthetic a priori knowledge. As content with out concepts and concepts without content are both empty notions.
What then is the aim of the Critique of Pure Reason? Kant attempts to steer a path between rationalism and empiricism while making reference to possible experience. Opposing Hume by demonstrating that synthetic a priori knowledge is possible and offering examples of such knowledge in order to counter act Humean skepticism. While also opposing the Wolffian-Leibniz view that reason alone can provide knowledge of the world as it is in itself. It is common for Kant commentators divide the Critique into two halves. The first being the 'Analytic' positive project showing the Humean skeptic how knowledge is possible. The second being the 'Dialectic' negative half showing how reason alone can not provide knowledge of the world.