Metaphor and simile are both figures of speech based on comparison. In other words, they bother discuss one thing by comparing it to something else. In the case of simile, the comparison is explicit, and in English usually uses the term "like" or "as" (e.g. "My love is like a red, red rose"). In the case of metaphor, the comparison is implicit ("The ship of state foundered on the reef of debt.")
One of the main purposes of metaphor and simile is to explain the unknown in terms of the known. For example, if a friend was wondering how frog's legs tasted, you might answer "They taste like chicken, but stringier and faintly fishy." If the friend know the tastes of chicken and fish but not of frog's legs, this comparison would explain the taste.
Sometimes figures of comparison are used in the opposite way, as a form of defamiliarization, comparing the familiar to something unusual or presenting the ordinary in an unusual way in order to make the reader think about something from a fresh perspective, i.e. as when Campion compares a woman's features to flowers in "There is a garden in her face" or when Shakespeare compares a poem to marble.