According to Google Defitinions, ERP system is:

• Enterprise resource planning (ERP) is a company-wide computer software system used to manage and coordinate all the resources, information and functions of a business from shared data stores.
• An ERP system is a business support system that maintains in a single database the data needed for a variety of business functions such as Manufacturing, Supply Chain Management, Financials, Projects, Human Resources and Custoemr Relationship Management.
• Enterprice resources planning. An accounting-oriented information system for identifying and planning the enterprise wide resources needed to take, make, ship and account for customer orders. 

All of these definitions have something in common and something different. Overall, I am pretty sure you could find an exact defitinion applicable to your situation - whether you are just starting with you business start-up, or if you are already running well established group of businesses.

As business evolves from small start-up, to larger companies, defitinion of "ERP system" can evolve from small accountancy software to somethign greater. Initial business requirements are to quickly record and correclty report various accountancy numbers. When business grows, you need more control over what goes in and goes out. Allowing customers to place orders, tracking shipments, sending automatic invoices, controlling marketing campaigns becomes necessary and of course, all these needs become part of your description of "ERP system".

We could relate to ERP systems as to expanding business

• Financial Management represents the core system and allow keeping track of and correctly managing company's finances. It's is vital a part when starting a business and a cornerstone answer for a question "what is an erp system?" - it is your business' accounting sofware.
• Sales & Marketing. As your business grows and you start selling more of your goods or services, you start spending more time with controlling sales orders. In order to assist you in automating most of the dull work "Sales & Marketing" comes into play. Depending on your ERP system, you have more control over how to create sales orders, how to invoice them, how to send invoices to client. Overall, increasing sales becomes part of your "what is an erp system" definition.
• Purchase Management. Increasing sales will mean, you need to buy more raw materials to produce your goods. Or to buy services from other companies. Therefore, increasing work on sales side literally means increasing work on the purchasing side. In order to deal with growing number of purchase documents you need to have purchase management system in place - which becomes a third cornerstone of "what is an erp system".
• Warehouse Management. Can you guess what happens when you start buying and sellings good in higher volumes? You are right! You need more space - therefore your definition of erp system naturally expands to Warehouse management. Can you see how your default ERP system, what was supposed to be only a simple accounting software is becomming something greater? Despatching goods, tracking them, confirming successful delivery, sending automatic PDF invoices - all of these tasks can (and should) be covered by "what is ERP system" definition.
  
• Manufacturing. If you are selling someone's else goods, you margins are quite low. And if you are selling more and more, you might consider expanding your business to manufacturing. However, then... calculating correct outputs, minimizing consumptions, figuring out costings - everything sums up into quite a difficult task which is solved by manufacturing module of ERP software.
  
• Projects. On other hand if you are not selling goods, but services, a different set of requirements come into play. Creating and tracking projects, calculating and mitigating risks, establishing and controlling contingency budgets - your needs changes drastically. Therefore, definition of ERP system expands with your requirements as well to cover project management.
  
• Resource Planning. Both in manufacturing and in project management you need to skillfully track your resources and efficient usage of them. Resourse planning module should assist you even further.
  
• Service Management. Expanding further into services? Need to meet high quality standards? Manages service processes for servicing items sold to customers.
• Human Resources. Even if you started out as one man army with your business startup, when expanding your business you will need to employ more people. With more employees, you need to keep track of human resources, their personal and professional information and qualifications.

With every business growth step a new set of requirements appear in horizont. However, with every new requirement, you can extend the definition of "ERP system" to apply it for your own business. And the best part is, that almost no one will be able to argue that!