Users are very creative in using tools. That is because they are not playing with the tool, they have a goal and work to do. Good tools are helping to get things done and this makes using it fun. Testing software according to the product creator's view is therefore only one dimension. To find more dimensions, testers use their imagination and employ creative techniques to run tests. On approach to test software to create better products is exploratory testing.

The term exploratory testing has been coined 1988 by Cem Kaner.

Exploratory software testing is a style of software testing that emphasizes the personal freedom and responsibility of the individual tester to continually optimize the value of her work by treating test-related learning, test design, test execution, and test result interpretation as mutually supportive activities that run in parallel throughout the project.

Cem Kaner. Defining Exploratory Testing. 2008

You can read more about exploratory testing in Elisabeth Hendrickson's book Explore It!

The projectdoc Toolbox, especially the add-on for software development, provides some templates to run exploratory tests.

Testers typically start with a test charter to define the mission, the tools, and the information of interest. During the test session they log all information they find. Some information is pursued immediately, some is noted for later sessions. At the end of the session a test report is presented to the interested stakeholders.