According to Webster’s English Dictionary, linguistics is “the study of human speech including the units, nature, structure, and modification of language.” This is a satisfactory general definition, but for the layman, it may be a bit too technical. You may not know what is meant by “units” in the description, nor “modification of language.” I will explain in some detail what the parts of the definition refer to.
“Human speech” refers to the way that people communicate. This in and of itself means a few specific things. It most obviously indicates humans, not robots or whales. The fields of study on how those kinds of systems communicate, while closely related to linguistics, are not the same. It is also mentioned later that this means the distinct parts of what has been said, from words to affixes.
“Units” refer to the building blocks of speech. Words, grammatical affixes, phrases, all fall under this part. In linguistics, the specific senses of these units are examined, as well as how they came to express such meanings.
“Nature” means, again, what individual units indicate. It also refers to natural processes, like language evolution. Thirdly, it may refer to the “nature” of a tongue, as in how non-speakers and native speakers of the language alike view the language.
“Structure” indicates how the language is put together to form coherent thoughts. From the internal structure of syllables to the order of words in a sentence, linguistic forms can be very complex and interesting.
Finally, “Modification of language” might convey two different things. It may mean the diachronic evolution of a language, like the progression of Old English to Modern English. It can also refer to the way that a tongue is changed to have a different meaning, like metaphor or analogy.