What is the difference between billable and non-billable expenses? Can you give a brief introduction of these two?

These terms are  usually related to the expenses incurred to perform any task on behalf of a third person.If the expenses incurred by a person/agent during the performance of a task is reimbursable from the principal/third person  vide issue of bill then it is a billable expense and if it is not reimbursable then it is not billable.In other words the above terms mean reimbursable and non reimbursable expenses.Whether the expenses is billable or not depends on the  mutual agreement between the parties. Billable expenses are recognised as expense in the books of the Principal)third person whereas non billable expenses are recognised as expenses in the books of the agent/the person performing the task.

The terms Billable and Non-Billable expenses are normally associated with say a consultancy company where they bill consultants out to their clients. Therefore Billable expenses will be paid by the client whereas Non-billable will be paid by your employer. What's included in both is subject to the contract your company has with their client.