You can capture business process specific information using custom forms.

For example, in the "Order Fulfillment Process", attributes like "Order Number", "Order Details", "Billing Information", "Ship-to Address" can be captured. A Lead Tracking process may need information like "Lead Name", "Referred By", "Time to make decision" , "Budget", etc.

A more powerful feature is the ability to capture custom data at each state transition not just at the first step. E.g. when moving a sales lead from "Waiting for Customer" to "Lost" you might want the sales representative to enter a "reason" on why they lost the lead while in a defect tracking process you may want the developer to attach a "test plan" when fixing a bug.