Pinning down the definition of "secular Buddhism" is not easy. If you've ever done some eel fishing it is a bit like trying to grab hold of an eel (my cousin and I used to fish for eels in the San Francisco bay).
First, it is important to get one definition of secular Buddhism out of the way. It is not about teaching Buddhism in a secular setting. If that were the case there would be no need for the adjective "secular" which is used by secular Buddhists to separate Buddhism, which is spiritual and religious, from Buddhism that is worldly.
The term 'secular' originally meant religious clergy who were not bound to the rules of a particular order; who were living in the world rather than in monastic seclusion. Not quite an oxymoron, but there were, in fact, secular clergy.
Turning to the formal notion of 'secularism', which is born in the 19th century, it opposes itself to anything spiritual or religious. Secularism believes that the nature of man and his moral duty can be deduced from man's temporal life which, by implication, includes his biological life. It is in some respects a kind of humanism except that it wants to exclude religion from society. In this respect, secularism is not without its ideological underpinnings. We get a taste of this from a quote by the National Secular Society founded by G.J. Holyoake in 1866 who coined the term "secularism": "We assert that supernaturalism is based upon ignorance and is the historic enemy of progress."
I believe it is in the context of Holyoake's idea of 'secularism' that we are to understand the thrust of secular Buddhism which certainly has a kinship with materialism and the belief in the omnipotence of the physical sciences. Given this bent, secular Buddhism, when we examine the literary output of its popular advocates is engaged in the work of revising Buddhism to such an extent that the Buddha’s message seems to be anti-religious and anti-spiritual. To be sure, secular Buddhists run far away from Frederick Heiler’s observation that Buddhism is the only really consistent form of mysticism.
The broader aim of secular Buddhist propaganda is to teach the moral teachings of the Buddha while, at the same time, leaving out his spiritual teachings when it comes to the subject of nirvana, for example. If we can imagine a secular Buddhist cannon it would be quite small as compared with its present size. All this assumes, in addition, that Asian and Indian Buddhists have been wrong ever since the Buddha died. But thanks to Westerners like Stephen Batchelor and John Peacock, true Buddhism has been rediscovered which naturally is secular (wink...wink...).