Where did Baptists get their name and what do they believe? Where and when did the Baptists get their name and what do they believe that sets them apart from the rest of Protestant denominations?

I realize there are different divisions among Baptists as well, so let's keep this limited to the issues that were relevant when the term Baptist first became used and that generally cover most Baptist denominations today but still specific enough to uniquely identify what makes Baptists different from the members of other denominations Protestant denominations.
The key difference is that in most other denominations (Anglicanism, Methodism, the United Reformed Church, etc) infant baptism is practised. Baptists believe that baptism is a public profession of personal faith - in other words, a public display of a decision someone has made themselves - and the notion of infant baptism is at odds with this.

Most new churches (emergent, or whichever word you prefer - churches that were established in the last few decades) profess to be non-denominational but tend to accord with Baptist theology, at least in the respect of baptism.