Explicit costs are reported in business documents. They are also known as direct costs. Explicit costs result in tangible assets for the company. Some examples are: rent, wages, maintenance. Explicit costs are easier to identify and account for because they leave a paper trail.
Implicit costs can be described as opportunity costs. Implicit costs deal with intangibles and do not leave a paper record. Implicit costs can be time or wasted opportunities, for example. An implicit cost is simply the loss of a possible benefit or asset that didn't occur.