Why he said that is important. If the db uses replication, the latest version that will support that is either 2013 or 2010 (I think the latter).
If the db in use is of type .mde or .accde ('compiled') then the up to date mdb/accdb version might be updatable but not the compiled version.
Some things/references/code may not work (e.g. old calendar control) or code may have to be modified to run on 64 bit Office if that's what's being used.
Is the db split (front/back ends)?
Whatever updating you attempt do NOT do it on the production version. Make a copy for experimentation.
The more we hear silence, the more we begin to think about our value in this universe.
Paraphrase of Professor Brian Cox.