An adVERB describes a verb, while an adJECTIVE describes a noun ( objects ,subjects inclusive).
The adverb is formed usually by adding LY to the adjective as in:
quick
quickLY
slow
slowLY
bad
badLY
Some adjectives stay the same in their adverb form such as :
hard
fast
Some exception is the adjective 'good' that becomes a different word as an adverb :
well
Examples showing the difference between adjectives and adverbs:
It is a quick jump .
'quick' is the adjective describing the noun 'jump'
He jumps quickLY
'quickly' is the adverb describing the action of jumping ,the verb 'jump'.
His hard work payed off.
'hard' is an adjective describing the noun 'work'.
He worked hard to get those grades.
'hard' here is an adverb describing the verb 'to work' in the past tense 'worked'.
It is a very good expression.
'good' ,the adjective describing the noun 'expression'.
He expressed himself well.
'well' is the adverb of the adjective 'good' ,describing the verb 'to express' ( expressed).
Hope the difference between both adverbs and adjectives is clear by now :)