For most visas the DIBP will want to check your Health & Character.
Depending where you are from and which visa you are applying for you may have to do medicals, and there’s different medicals for different visa types. Usually temporary visa’s have simpler medicals, while when applying for a permanent visa you have a tougher medical to do.
One tough element about medicals is that when you apply there is a “if one fails, all fail” rule, so if you have a member of your family with a serious medical condition (contagious, or costly) then this may prevent any of you from applying for permanent residence in Australia.
Character, as the name suggests, is a check of your character. This isn’t about whether you are a nice person, or an honest person, it’s about whether or not you are a criminal (or have a criminal past). While obviously we encourage everyone to avoid a life of crime, one key point is whether you have ever served a sentence in prison, and if so how long for, and how long ago it was. If you just got out of jail for a 10 year stretch then the chances are Australia is not going to welcome you with open arms.
However, don’t worry, if you have parking or speeding tickets, that’s not a crime…