Respecting plants involves seeing them as valuable beings on their own terms, and not just as sources of raw materials for human use. It means that plants deserve moral consideration in all of the ways in which people interact with them.
Actually, this is not a new idea at all! In many cultures, past and present, plants are treated with honor and respect.
There are many books, articles, videos, and audio recordings that provide valuable background on this topic.
A good starting point is a 50-minute radio show "Plants as Persons" from To the Best of Our Knowledge that aired December 19, 2020 and includes interviews with Robin Wall Kimmerer, Matthew Hall, Monica Gagliano, and Brooke Hecht.
Here is a range of recommended resources:
Monica Gagliano, Thus Spoke the Plant (Berkeley, CA: North Atlantic Books, 2018)
David Haberman, People Trees: Worship of Trees in Northern India (New York, NY: Oxford University Press, 2013)
Matthew Hall, Plants as Persons: A Philosophical Botany (Albany, NY: State University of New York Press, 2011)
Robin Wall Kimmerer Braiding Sweetgrass: Indigenous Wisdom, Scientific Knowledge, and the Teachings of Plants (Minneapolis, MN: Milkweed Editions, 2013)
Florianne Koechlin, Tomatoes talk, birch trees learn – do plants have dignity?, TEDxZurich video. (January 2016)
Stefano Mancuso and Alessandra Viola, Brilliant Green: The Surprising History and Science of Plant Intelligence (Washington, DC: Island Press, 2015).
Michael Marder, Plant-Thinking: A Philosophy of Vegetal Life (New York, NY: Columbia University Press, 2013)
Michael Pollan, The Botany of Desire: A Plant's-Eye View of the World (New York, NY: Random House, 2002)
Suzanne Simard, How Trees Talk to Each Other, TED Talk video, (June 2016)
Christopher D. Stone, Should Trees Have Standing: Law, Morality and the Environment (Third Edition) (New York, NY: Oxford University Press, 2010)
Paul Taylor, Respect for Nature (Princeton, NJ: Princeton University Press, 2011 (first printed 1986))
Anthony Trewavas, Plant Behaviour and Intelligence (Oxford, UK: Oxford University Press, 2014)
James Wandersee and Elisabeth Schussler, “Toward a Theory of Plant Blindness” Plant Science Bulletin, 27(1), (2001) - Pages 2 - 9.
Peter Wohlleben, The Hidden Life of Trees (Vancouver, BC: Greystone Books, 2016)