Honestly, I don' t know so much about enterprising computing and information technology (IT) so rather than stumble through my answer, I turned to my colleague and IT expert Paul Dube, head of Align IT Advisors.

Here's how he explains ERP:

ERP stands for Enterprise Resource Planning and is a combination of Accounting software (think Quickbooks - not Quicken), Sales Order Processing- order entry, shipping, invoicing, Inventory Control, Manufacturing Resource Planning, manufacturing Scheduling, Shop Floor Control (work order) software and often CRM - Customer Relationship Management.

For Process driven companies like Pharmaceuticals or Chemical, it would have 'recipe' and 'batch' controls and for Project companies like Construction, it would be 'project' control rather than 'shop floor' control. It can be monolithic or modular, client/server or web based.

Companies use it to keep track of their business. The bigger the company, the more they need to manage it with such software as it give them all of the views into what is happening in the business. It keeps track of gross margin, how long it takes to collect an invoice, etc.

What is surprising to me is how few systems include 'Executive Information' systems or 'dashboards' where the top executives get a high level view but can drill down to any level of detail necessary.

With its typical love of jargon and buzzwords, Wikipedia describes ERP thusly:

Enterprise resource planning is a term derived from material resource planning. ERP systems typically handle the manufacturing, logistics, distribution, inventory, shipping, invoicing, and accounting for a company. Enterprise Resource Planning or ERP software can aid in the control of many business activities, like sales, delivery, billing, production, inventory management, and human resources management.

ERPs are often called back office systems indicating that customers and the general public are not directly involved. This is contrasted with front office systems like customer relationship management systems that deal directly with the customer.

ERPs are cross-functional and enterprise wide. All functional departments that are involved in operations or production are integrated in one system. In addition to manufacturing, warehousing, and shipping, this would include accounting, human resources, marketing, and strategic management.
In the early days of business computing, companies used to write their own software to control their business processes. This is an expensive approach. Since many of these processes occur in common across various types of businesses, common reusable software may provide cost-effective alternatives to custom software. Thus some ERP software caters to a wide range of industries from service sectors like software vendors and hospitals to manufacturing industries and even to government departments.

Here are a few more resources to check out:

• List of open source ERP solutions
• Wikipedia's own list of ERP vendors

Hope this helps you understand this critical corporate IT infrastructure element.