When invoicing you would go through Invoicing - Create Invoice to get to the New Invoice Batch page. The check boxes next your client/project are to choose which clients and projects you would like to invoice.
Once you check the box next to a client or project you will see check boxes populate in the center and to the right. The center two boxes are for your Labor and Expense Items. This comes in handy if you would like to create an invoice for just the expenses, so you would uncheck the box next to your Labor items for example and click Save to create the invoice.
The boxes to the right come in handy if you are working with multiple Projects under a client. If unchecked it means that each project will show on one invoice, sub total per project, and grand total at the bottom. If checked, it means that each project will be shown on separate invoices.