Illegal streaming is streaming illicit copies of any content, including films, TV shows, or sports, without the copyright owner's permission. This can include watching illegal content using an add-on accessed from a device like a set-top box or a stick, streaming from an unauthorised website, or streaming via an app (on a smart TV, mobile phone, tablet, laptop or games console).
Streaming hardware devices like set-top-boxes or Amazon Firesticks / Google Chromecasts in their unaltered form are legal - but many are being modified and then sold, with unauthorised add-ons pre-installed that allow people to access, stream and watch copyrighted content illegally. Elsewhere, through social media sites like Facebook & YouTube, illicit links and streams to pirated film/TV & sports content are posted without the copyright holder's permission.
Finally, whilst using a Virtual Private Network (or VPN) to add extra security to your online data is perfectly legal, it is against the vast majority of streaming platforms' terms of service to use a VPN to unlock content specifically unavailable within your own country. Some examples of pirated content are films that are not yet released in the ROI, TV programmes that haven't aired yet or that are only being shown in the ROI on streaming services for which you don't have an account, pay-per-view offerings for which you have not paid and sports events that are aired legally only on sports channels for which you do not have a subscription.
In short, if you are streaming and watching films, TV or sports content through an unauthorised source - for free or paid-for - then you are streaming illegally.