Part-of-speech tagging, also known as grammatical tagging, is the process of marking a word in a text as corresponding to a particular part of speech, such as noun, verb, adjective, etc., based on both its definition and its context. This is an important step in the process of natural language processing and computational linguistics, as it provides a deeper understanding of the syntax within a text.

Part-of-speech tagging is used in many areas of computer science and artificial intelligence, including machine learning, text-to-speech conversion, and more. It is often used in the process of training language models, which are used in tools like autocorrect and predictive text.

Consider the sentence: "The quick brown fox jumps over the lazy dog."

Here is a step-by-step part-of-speech tagging of this sentence:

1. "The" is a determiner (DT). Determiners are words that precede and modify a noun, specifying its reference in context.
2. "quick" is an adjective (JJ). Adjectives are words that describe or modify other words or phrases.
3. "brown" is also an adjective (JJ).
4. "fox" is a noun (NN). Nouns are words that represent a person, place, thing, or idea.
5. "jumps" is a verb (VBZ). Verbs are action words. In this case, "jumps" is in the third person singular present tense.
6. "over" is a preposition (IN). Prepositions are words that express spatial or temporal relations.
7. "the" is a determiner (DT).
8. "lazy" is an adjective (JJ).
9. "dog" is a noun (NN).

So the part-of-speech tagging for the sentence is: The/DT quick/JJ brown/JJ fox/NN jumps/VBZ over/IN the/DT lazy/JJ dog/NN.