In the line, "O My Luve’s like a red, red rose," by Robert Burns, which figure of speech is this an example of?

This line is an example of a simile.  A simile is a comparison, usually using "like" or "as."  This can be distinguished from a metaphor, in which we are saying something is something, not simply like something.  Both similes and metaphors play an important part in writing, so that people can have concrete imagery to focus on.  Here are some examples of similes and metaphors for you, so you can understand the difference.

Similes:

Her...

This line is an example of a simile.  A simile is a comparison, usually using "like" or "as."  This can be distinguished from a metaphor, in which we are saying something is something, not simply like something.  Both similes and metaphors play an important part in writing, so that people can have concrete imagery to focus on.  Here are some examples of similes and metaphors for you, so you can understand the difference.

Similes:

Her hair was like golden sunshine. 

He was like a feral wolf.

The crowded, cluttered house was like a flea market.

Metaphors:

Her hair was golden sunshine.

He was a feral wolf.

The crowded, cluttered house was a flea market.

In similes and in metaphors, I am trying to show that the subject has some attributes of what follows.  The reader knows that the hair is exceptionally bright, like the sun, that the man is wild, untamed, like a wolf, that the house is so crowded and cluttered, it has the attributes of a flea market.  Without similes and metaphors, our language would be impoverished!