As Bubblehead previously mentioned, it's typically called a "local level" hearing, and is part of the grievance process. Local hearings typically involve you, the labor manager(s) and your business agent(s). Your union steward as well as local management may also participate, should they desire (though UPS makes it difficult for union stewards to do so).
In the case of a termination, the Company will present its case and then you'll have a chance to respond. After the presentation, the Company will make a decision regarding your grievance. Typically, for a working discharge, this means it will be reduced to a warning or suspension. If you're adamant that you did nothing wrong and refuse to accept any discipline (especially in cases in which back pay is wrong), typically the Company will deadlock with your business agent and the case will proceed to panel. (It snows in Las Vegas -- and yes, it does snow in Las Vegas -- as often as UPS "admitting" it was wrong... even if it was wrong.)
BTW, your business agent can "predict" the outcome of the local level meeting - with surprisingly accuracy -- before it takes place.