Secularism can be understood in two quite different ways, often described as 'hard secularism' and 'soft secularism'.
Hard secularism. Some people, sometimes operating from a religious perspective and sometimes operating from a strongly humanistic perspective, see secularism as a powerful enemy of religion, a tool to remove religion from the public view and ensure it is only practiced between consenting adults behind closed doors. In this sense, the term is often used (confusingly, in my view) as a synonym of 'humanism' (as, for example in this Guardian article: 'UK secularism on rise as more than half say they have no religion') [see Humanism].
Soft secularism. Other people see secularism as a vital protector of religious and political freedom, ensuring that competing beliefs and ideologies can communicate freely and fairly on a level playing field. Used in this sense, this community and website can be accurately described as a secular project.
The term 'secularism' was originally used in the soft sense; according to Wikipedia, the word was first used this way by George Holyoake in 1851, but the idea of soft secularism goes back much further. John Locke argued for it, but so too did the Anabaptists and other Christian groups, stretching right back to the very first Christians.
Many people consider that the basic meaning of secularism is the belief that the state should operate separately from religion. This is arguably always important, but it is particularly important where there is one dominant religious system which seeks (or simply expects) to have a significant and persuasive voice in the activities of the state.
The actual concept of secularism is not a simple one: in my experience, people who think it is simple have rarely actually discussed it, and have tended to make the easy assumption that the meaning they give to the term is the same meaning that all reasonable people use. But when you affirm that there should be separation between state and religion, you are using three complex ideas: 'state', 'religion' and 'separation'. Separation from religion is not the same as separation from spirituality, and separated things may influence one another, even if they do not control: separation is not the same as total disconnection.
Some of the issues and confusions which arise when people do not clearly distinguish between these two forms of secularism can be seen this this TED Talk by David Voas: 'Why there is no way back for religion in the West'.
After the international secularism conference in 2014, Peter Tatchell posted the 'Manifesto for Secularism – Against the Religious Right'. It contains some good and helpful conent, but also some confused and questionable content: here is a short response to the manifesto.