A mildly derogatory term for someone (normally but not necessarily, female) who is mistreated and put-upon. A doormat is normally not happy with their life but will often not do anything to change it due to low self-esteem and perceived lack of options. A doormat is not a BDSM role but the term does crop up now and then in comparison.
From an external, vanilla perspective, it can be confusing to realise the difference between a doormat and a sub or slave. Perhaps they both are spanked when their partner wishes, made to do tasks they would rather not, restricted in their behaviour and even speech. Fundamentally, the difference is one of willingness and consent (at some point - consent would normally be a once-off event for a slave). Look closer and the differences become very much more obvious: the doormat is normally unhappy, not encouraged as a person, lacking in self-esteem; the BDSM submissive is (on the whole - nobody's life is perfect) lively, happy with her/his lot, proud of her/his partner and full (often very full) of confidence.