All of the above involve verifying and validating our certain expectations or fears (positive and negative testing) associated with the target that we are dealing with. These actions help us reaffirm our belief in the outcome that we expect, makes us tad little more comfortable. Comfortable in the realm of the related risk and cost associated in case of finding a "bug" later after the ownership is transferred to us. Thus the intensity and complexity of the testing varies based on the risk and cost. For example we should be comfortable if told that the sofa-set that we buying is tested to the effect of 99%, we may not feel the same if our airline says same thing for the aircraft that we are going to board (are we going to ask whether this is the 100th flight??!!)
Out need to test arise from the fact that we are humans and we can make mistakes, even machines can go wrong at times. We need to ascertain that the product or the process is as per the defined guidelines and standard, this leads to quality associated with the product. Higher the percentage at which the tests pass, higher is the quality. So essentially we are assuring the quality that we expect from the object under test. Also, to ensure the element of manual defect does not creep in, we tend to automate the tests, especially in case of the multiple repetitions of the test cases under various data sets and scenarios. This leads to test automation and agility in the quality assurance process.
I shall write some more associating the technology of testing and automation concepts with our daily lives. But aren't we all testers here?