DE (地) is a pre-verbal modifier that works with adverbial phrases. It is used after an adjective to form an adverb, describing the degree of the action (i.e. the verb). The structure is similar to English, in which some adjectives can be combined with suffix -ly to form adverbs.
mā mā xiǎo xīn de zǒu
Mom walks carefully.
In contrast, DE (的) is a pre-head modification marker. The modifier precedes DE (的) is normally an adjective modifying the head noun.
xiǎo xīn de rén
a careful person