A union is nothing more than the coordinated resistance of employees against employer rule. For example, if your boss tells you to do something unsafe, and one or more of your coworkers is willing to stand by you in your refusal to obey, whatever this may entail, that is a union. That is how unions began, and it is fundamentally what makes unions important.
Whether or not your challenge to the boss's authority has been preapproved by your employer's representatives in government is a whole other consideration. But it is worth mentioning that this what 90% of the discussion about "unions" amounts to in the United States. By this criteria, a "union" and its activities are legitimated and regulated by politicians, who in turn decide what kind of resistance will be tolerated by law. In a class society, we can imagine a scenario where politicians, influenced by the economic monopoly held by employers, end up restricting most of the types of activity that give employees and their communities real strength in the face of employers. Long story short, this explains a lot about why mainstream unions are deficient: in a word, they suck. But that has more to do with the profound disadvantage they sustain just as soon as they gain "legitimate" status in an employer-run society than it does with some special failing amongst labor leaders (i.e. the two happen in succession).
Most US unions are run on the employer-sanctioned "business union" model, which basically turns unions into businesses themselves. These unions serve as legal representation in relations between employers and employees. Employees pay dues, and the business union provides the "service" of talking to your boss when you have a problem, or negotiating what is called a "collective bargaining agreement" -- a contract which spells out raises and work rules, and so on, for a given period of time. Basically, you pay money, and your union representatives "represent" you.
In contrast to business unionism, there is something called solidarity unionism. Solidarity unionism is a model which seeks to advance the interests of all employees as a class. We know that when we talk about "class," we are talking about a very inclusive concept: the "working class" is everyone compelled by economic necessity to work for anybody else. Solidarity unionism sees unions as an outgrowth of community concerns which happen to find their expression in the workplace. In other words, unlike business or what is called "craft" unionism, solidarity unionism is opposed to the narrow pursuit of economic advantage for certain parts of the workforce vs. others. Traditionally, this orientation has worked to bring the conditions of the poorest and most vulnerable up to the standards of others in the labor market, while at the same time demanding an end to "wage slavery" altogether.
Because solidarity unionism is informed by a class perspective, it understands that the role of government in very unequal societies is to defend the wealth of the haves against the needs of the have nots. We see this playing out in particular splendor as of late: the bankers who wrecked the economy keep their contractually stipulated bonuses, while their political servants wail that school teachers are bankrupting the nation! Limited government, predictably, has meant limiting governmental utility for the working class, while at the same time increasing governmental aid to the nation's owners. For this reason, solidarity unions are reluctant to be drawn into legal contracts with employers, since a union's real strength lies not in governmental mediation, but in the original spirit of what unions are all about.