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Many gnuplot terminals (aqua, pm, qt, x11, windows, wxt, ...) open separate display windows on the screen into which plots are drawn. The persist option tells gnuplot to leave these windows open when the main program exits. It has no effect on non-interactive terminal output. For example if you issue the command
gnuplot -persist -e 'plot sinh(x)'
gnuplot will open a display window, draw the plot into it, and then exit, leaving the display window containing the plot on the screen. You can also specify persist or nopersist when you set a new terminal.
set term qt persist size 700,500
Depending on the terminal type, some mousing operations may still be possible in the persistent window. However operations like zoom/unzoom that require redrawing the plot are not possible because the main program has exited. If you want to leave a plot window open and fully mouseable after creating the plot, for example when running gnuplot from a script file rather than interactively, see pause mouse close.