Core aeration is a process in which you aerate the lawn by
remove plugs (cores) from the soil. This can be done with a
reasonably small power machine or it can be done with a
manual shovel-sized tool which only removes 2 plugs at a time.
In either case, the holes are about the size of your little finger.
When you roll the lawn, any areas which have been core aerated
will compact lower than the rest of the lawn since those areas now
have less total soil.
Any machinery heavy enough to ruin your septic field is heavy enough
to ruin your lawn. You don't want equipment heavy enough to roll
asphalt, just something that does some light compaction of the soil.
This info is probably covered in great detail in gardening-oriented
newsgroups. Also, a trip to the library is probably a good idea since
many lawn & garden books cover this in detail.