A read-eval-print loop (REPL) is an interactive environment that reacts to user-input. REPL-driven development is a very interactive programming style with a short feedback cycle enabling developers to evolve their projects and try new features quickly.
Tools like MatLab, RStudio, Gnu Octave are REPL-based because one of their major use-cases is (scientific) experimentation and exploration for which short feedback cycles are essential. For example, imagine a data-scientist has the task of correlating data samples in a meaningful way. At the beginning, she may not know herself which machine learning algorithm is most suitable for the problem at hand; she may want to try different ones to see which one fits best. In a non-interactive environment, this would be laborious as the scientist would waste a lot of time by changing and re-running the code for her experiment whereas with REPL-based development, she could just try to apply her ideas with inside the interactive environment with instant feedback.