A noun is anything that you can see, touch, smell, hear or think about. Verbs, on the other hand, are "action" words. While a noun may not be tangible, a verb cannot function without a noun.
So, for example, imagine a hamster is running on a wheel in your house. The hamster and the wheel are both nouns, as is the feeling of futility he gives you, as that is an idea. The running, however, is a verb. It is different from the futility because it cannot exist without the hamster and his wheel. "Running" has to have someone actually carrying out the action it describes, while a hamster simply needs to exist.
Pronouns are "substitute" nouns like "it," "he," "she" and "they." They are used to save repetition and make your writing less awkward, particularly with larger words.
An adjective is a word that describes a noun, while an adverb is a word that describes a verb. So, for the example above, an adjective could be added by writing "the white hamster ran in the wheel." The adjective is "white" as it is describing the hamster.
You could add an adverb by writing "the white hamster ran quickly." "Quickly" is describing how it ran. To use an adverb in its other form you can write "the very white hamster ran quickly." The adverb "very" is defining precisely how white the hamster is.
Interjections are one of the easier parts of speech to remember -- they are one-word sentences that convey an emotion. "Stop!" is an interjection, as is "No!" They are given their own part of speech because they have to function in an odd manner, as one-word sentences without subjects, verbs or objects. They are a matter of how the word is used rather than what it is: "The man told him to stop," for example, is using "stop" as a verb rather than an interjection.
Conjunctions, prepositions and articles all work with other words to describe how they relate to one another. Conjunctions connect two sentences that could otherwise stand alone: "the hamster ran on the wheel, but he was not happy" is two thoughts that are combined with the conjunction "but" in order to make one clear sentence rather than two awkward ones.
Prepositions, on the other hand, connect words and thoughts by showing how they relate to one another. "The hamster in the wheel was running" shows how the hamster and the wheel are related -- the hamster is inside the wheel. As opposed to conjunctions, the two thoughts that are joined could not stand alone.
Finally, articles describe two words: "a" and "the." "A" is an indefinite article as it just refers to a generic noun: "A hamster was in the cage" could be describing any hamster. "The," on the other hand, is a definite article. It refers to one specific noun and therefore makes the sentence more noun-focused. "The hamster was in the cage," makes it clear that a specific hamster is being referred to.