IR35 is legislation used by HM Revenue and Customs to stop companies using intermediaries to avoid paying the correct tax and National Insurance.
Previously, employees could avoid being taxed by offering their services through a company, which acted as a middle man, then taking funds from the his company in the form of a dividend instead of a salary. This meant that National Insurance contributions and standard PAYE didn't apply, leaving the individual to pay a much lower rate than was actually due.
IR35 means that in scenarios like this, the correct tax is paid and eliminates the advantages of offering services through a false, 'middle man' company.
Here are the cases where IR35 applies.