There's two primary benefits to being in a union in a non-unionised environment. The first is access to the union's legal resources, you can usually get free advice on employment matters from qualified solicitors, and in the event of an actual tribunal or court case related to your employment, you get the union's solicitors instead of whatever solicitor you can afford on your own. The second is representation at disciplinary hearings. You always have the right to bring a companion to disciplinary hearings, who can present your case for you and sum up your position, and talk to you and give you advice on how to proceed. As a union member, you get to bring a union representative to these meetings, someone who has been specifically trained by the union to deal with these hearings.
In my personal experience the latter is even more powerful when a workplace is not unionised. In unionised workplaces, management will get training on how to handle the rep, and will ensure they have an ironclad case before they step into the meeting room. In non-unionised workplaces where most disciplinaries involve the employee meekly submitting to the person holding the meeting, managers have no experience of what to do with a rep present and the union rep usually takes them apart.