Why are adverbs/ adjectives important in developing a story's character? What does it insinuate upon the reader?
First, adverbs and adjectives are two different kinds of descriptive modifiers and should not be confused with one another. Adjectives modify nouns ("a red ball"). An adverb usually modifies a verb ("he ran quickly") and sometimes an adjective ("he was incredibly smart"). As a general rule, adverbs are best used sparingly. For example, if a strong verb is used, it may not require a modifier. Thus, instead of "he ran quickly" you can more effectively write "he sprinted."
Your question is perhaps better posed as, "How can descriptive language be used to develop a story's character?" Descriptive language, after all, can include verbs. For example, "He shuffled into the room" is more descriptive than "He walked into the room."
Descriptive language is pivotal in developing a story's character. It can be used to bring to life three different aspects of a character:
1) their appearance
2) how they speak and act
3) how they see the world
The first two are fairly obvious and straightforward, but the third is more difficult and elusive. Basically, every character - depending on their age, gender, class, occupation, etc. - will see the world through a different lens. Thus, the language used to describe their thoughts and perceptions should reflect that particular lens.
For example, say you are describing a character walking into a room for the first time. If your character is an interior designer, he may notice the wallpaper and the color scheme. If he is a photographer he may notice how the room is lit. If he is a writer he may look to see what books are on the shelf. These are all subtle ways of showing rather than telling who your character is.
Adjectives and adverbs are important in terms of description and the extra information that they provide and how they are used to build up imagery. If you want to know what they add and contribute, try this simple exercise. Find an excellent extract from a short story with lots of adverbs and adjectives, then write it out, taking away all of the adverbs and adjectives. You will see how the adverbs and adjectives add so much colour and force and personality to the writing. Consider the following example from "Marigolds" by Eugenia W. Collier:
When I think of the hometown of my youth, all that I seem to remember is dust--the brown, crumbly dust of late summer--arid, sterile dust that gets into the eyes and makes them water, gets into the throat and between the toes of bare brown feet. I don't know why I should remember only the dust. Surely there must have been lush green lawns and paved streets under leafy shade trees somehwere in town; but my memory is an abstract painting--it does not present things as they are, but rather as they feel.
Read this quote once without the words in bold, and then once with. You can see that these adjectives and adverbs are essential for building up our impression and feelings about the dust, and also creating the contrast between the actual memory of the narrator and the green paradise that she knows must have been part of her childhood. Adjectives and adverbs are therefore key in building up tone, mood and an overall image of the work.