When the SMSF member dies their remaining benefits in the SMSF become their "death benefits". 

These death benefits remain in the SMSF and don't automatically become part of the member's estate, similarly / or different in ways to the member's interests in a discretionary or unit trust, which can be dealt with specifically in the member's will subject to the relevant trust deed allowing for the passing over of the person's interests in the trust (except for office holdings which are personal).

A binding death benefits nomination ("BDBN") appears as an often two page form, compared to the length of the person's will which can be many tens of pages long.

The BDBN binds (or by broad description "instructs") the trustee of the SMSF to distribute the member's death benefits to a particular death benefits recipient beneficiary (and there are restrictions from a SMSF compliance and from a tax perspective on who those recipients can be - i.e. a spouse or child mainly) or to the member's estate (their "legal personal representative" or "LPR"). 

A BDBN can be (overly simply) described as "A to B".

But understanding a BDBN requires comparison to other things that are not BDBNs such as non-binding death benefits nominations ("non-BDBNs") and reversionary pensions. Something also that is not a BDBN is a BDBN form that is not completely signed in accordance with the requirements in the SMSF deed.

A reversionary pension ("RP") is a change to a pension entered into while the member is alive to be paid to the member that changes or "reverts" to their reversionary pension recipient beneficiary (e.g. their surviving spouse) but the payments of the pension still constitute death benefits of the deceased member (e.g. a death benefits pension entered into after the member has died). 

The SMSF deed needs to clearly set out, if the member has both a RP and a BDBN in place whether the BDBN overrides the RP to take all of the member's death benefits or whether the RP continues to separate some of the member's death benefits to continue paying the pension to the reversionary beneficiary.

A non-BDBN is not binding on the SMSF trustee and can be taken into account by the trustee (or a court, see Lynn v AFCA) or completely ignored (see Tratter). The outcome of a non-BDBN can be very different to a BDBN, it is uncertain, it can be taken into account or can have zero value. 

But a non-BDBN (which is often provided for free at the back of the SMSF deed) can be mistaken for a BDBN, especially if the member is not aware that there even is a difference.

The difference between the non-BDBN and BDBN will also be determined by the provider that drafted the SMSF deed you use. Therefore there could be no universal explanation of the differences between a BDBN and non-BDBN compared to its difference to a RP (i.e. the RP pays a pension and the BDBN/non-BDBN pays a lump sum) as the differences can differ between SMSF deeds (apart from the BDBN should be binding and the non-BDBN is not binding).

In the end a BDBN gives certainty that A will get to B (if it is signed properly) and the non-BDBN (which is generally easier to sign) gives no certainty.

Generally a BDBN won't be given for free because the signatures on a BDBN must be checked by a lawyer to ensure it is signed properly.