So, what is language? I do not intend to deal with phenomenological or ontological issues. This is just a witggensteinian approach (the meaning of words is its (conventional?) use). I simply want to point out two facts: 1) Those of us who work as English as a foreign language teachers cannot teach (or at least are very unlikely to succeed and are much more ineffective) if we do not even know or ask ourselves what language is; and 2) our conception of language is not one single monolith.
My very personal, most favorite definition is that “language is the evolutionary mechanism that humans developed to achieve ‘shared cognition’ (a common consciousness with the others).” But that is something to be discussed at some other moment with much more theoretical machinery from the cognitive neurosciences that define the underpinnings and differences between sensation, perception, and conception.
I did not tackle the "language is grammar" conception for this seems to me way too reductive. I am quite open, though, to discussing this as a possible component of the conceptual prototype of what language is.
The level of schematization is gargantuan: ¿How do we craft a definition that takes into account all the spaces-times in which language inhabits?
I did not cite any specific authors in my initial reasoning of six conceptual waves for there are too many researchers within each wave; nevertheless, for novice learners, I could suggest the following as a starting point in case you would like to dig deeper into these matters:
Language as a means of communication: Reddy, M. J. (1979). The conduit metaphor: A case of frame conflict in our language about language. In A. Ortony (Ed.), Metaphor and Thought (pp. 284–310). Cambridge University Press; https://www.academia.edu/6290150/The_Conduit_Metaphor_A_Case_of_Frame_Conflict_in_Our_Language_about_Languag
Language as a conceptualization system: Talmy, L. (2000). Toward a cognitive semantics. MIT Press; https://www.acsu.buffalo.edu/~talmy/talmyweb/TCS.html
Language as a social construct: Silverstein, M. (2004). “Cultural” concepts and the language-culture nexus. Current anthropology, 45(5), 621-652. http://mapageweb.umontreal.ca/tuitekj/cours/SilversteinCA2004.pdf
Language as symbolization: Langacker, R. W. (2008). Cognitive Grammar-A Basic Introduction. Oxford University Press. https://edisciplinas.usp.br/pluginfile.php/258516/mod_folder/content/0/v.%20langacker%20Cognitive-Grammar-An-Introduction.pdf?forcedownload=1
Language as words: Kenneally, C. (2007). The first word: The search for the origins of language. Penguin. https://drive.google.com/file/d/10p6Vj0Tkaox6AoPnIdOXI-WZU1VfeH2i/view?usp=sharing
Language as an indoctrination: Harris, R. A. (2021). The linguistics wars: Chomsky, Lakoff, and the battle over deep structure. Oxford University Press. https://drive.google.com/file/d/1hI5wq7Y8DeC1Ny50XB3bP42zHwFS56F5/view?usp=sharing
For Langacker (1987), symbols are not 100% arbitrary. He illustrates this with the word "stapler," which is arguably composed of two morphemes: "stapl-" and "-er." Since "-er" carries schematic meaning of its own, the symbol "stapler" is not 100% arbitrary.
Excerpt from Langacker (1987):