An Open-Ended Text is a question type that allows the respondent to type in the correct answer. It only allows a limited amount of space for typing in the answer. The test administrator can specify the correct answer when creating this type of question.
Lets say you didn't want your respondents to be able to see the correct answer, as is done with multiple choice questions. An Open-Ended Text question would allow you to ask almost any question and require the respondent to type in the correct answer.