Let me start out by saying that I'm speaking about The Kanban Method as pioneered by David J. Anderson and that I am the Program Director for the KCP program at LeanKanban University.
David has been on the record numerous times as saying that The Kanban Method is not an Agile software development methodology, but rather a methodology that is an alternative path to agility.
The distinction is important because very often we see organizations adopt an defined Agile method (Scrum, DSDM, XP, etc) but are not agile. They are performing the rituals but have not embraced the values and mindset required to be agile. So in these cases, the adoption of the Agile methodology was intended to be a path to becoming an agile organization.
The Kanban Method is significantly less prescriptive regarding what you have to do from a ritualistic point of view and focuses more on observable improvements in service delivery and experimenting with numerous kinds of practices. As an example, a team may not feel that weekly sprints are helpful and want to move to a continuous flow model. The simplest experiment might be to move to on-demand (or more frequent) queue (sprint backlog) replenishment and see if that made the team more effective in providing services to the customer. If it didn't work, we'd roll back the policy change and try something else to improve the teams capability.
The important distinction is that the goal of The Kanban Method is to improve an organization's or team's ability to provide services to downstream partners (customers) in the workflow, using any practice that demonstrates an improvement. So we use The Kanban Method to achieve organizational agility vs seeing it as an Agile method that can be installed.
From a practising point of view, you'll often see well-functioning Kanban teams and Scrum teams looking very similar because may of the practices are just good things to do. The Agile Manifesto is as valuable a guide to good behaviour for teams when you are talking about software development. Kanban also works in non-product development situations such as marketing, digital content creation, legal workflows, etc as described in numerous white papers from our LeanKanban conference series.
If you'd like to review my thoughts on the practical differences you'll see between two software development teams practising Kanban and Scrum, please check out this blog post as well.