Professional year in Australia is usually a reference to someone who has done a professional course and to be fully recognised/registered with a professional association, they do what is often called a Professional Development Year, often associated with some medical occupations where it is deemed appropriate that someone gets a year under supervision.
There may be variances on the meaning depending on the context the reference is in.
If you click on the language heading or any heading for that matter in the eligibility table you will be taken to explanatory information.
The professional year program is a special program which was designed by the government and is only for international students who finished their Accounting, IT or Engineering degree in Australia, applied for a 485 visa and have an IELTS of at leat 6.0. The program is a 44 week program and it's all about australian workplace, business communication skills classes followed by a full time 3 months internship. The idea is to make international students in Austrlaia more employable.
There are few providers who offer this course, one of the biggest in Professional Pathways Australia which is owned by Monash Uni.