What is the role of Utility Methods in Salesforce ?

Utility classes are helper classes that consist of reusable methods. This method is like you have any other apex class, where you have written some code and you can use those methods in Trigger.

Example:

trigger updateOpp on Opportunity (before insert){
 for(Opportunity  opp : Trigger.new){
 opp.formattedDate__c = TriggerHelper.formatDate(opp.someDate__c);
}
}

//Utility Class
Public Class TriggerHelper{
Public Static string formatDate(Date inputDate){
   return inputDate.format();
}
}

Utility Class, also known as Helper class, is a class, which contains just static methods, it is stateless and cannot be instantiated. It contains a bunch of related methods, so they can be reused across the application. As an example consider Apache StringUtils, CollectionUtils or java. lang.