An expression of interest (EOI) is a way of showing your interest in applying for a skilled visa to immigrate to Australia. It is an online form in SkillSelect which asks a series of questions about your skills depending on the visa subclass that you are selecting to apply for.
The EOI is used to calculate your ability to meet the points test for certain skilled visas. It is available for Employers and State/Territory Government agencies should you like to be considered for a sponsored skilled visa.