Who are Pyramus and Thisbe in A Midsummer Night's Dream by Shakespeare?

Pyramus and Thisbe are characters in the play the craftsmen are performing.
The characters of Pyrmaus and Thisbe (or Thisby), are characters from the Roman poem Metamorphoses by Ovid.  Their story is similar to that of Romeo and Juliet.  They were two young lovers whose parents kept them apart, and they met an untimely end.  Why someone would choose this play to present at a wedding is beyond me.
The play Pyramus and Thisbe is being presented by the craftsmen, a group of men with no acting experience.   They are presenting it at the royal wedding of Theseus and Hippolyta, so they really want to get it right.  They don’t want to offend anyone. 
Quince, the leader, introduces the play as a “lamentable comedy” and passes out the parts. (Irony means nothing to Quince.)  He assigns the lead, Pyramus, to the pompous Bottom.

BOTTOM
What is Pyramus? a lover, or a tyrant?
QUINCE
A lover, that kills himself most gallant for love. (Act 1, Scene 2) 

Flute is assigned the role of the girl.  In those days, all roles were played by men, and this group is all men anyway.  Shakespeare makes a joke about the fact that young men often played the female roles when Flute says he can't play the girl because he is getting a beard. 

QUINCE
Flute, you must take Thisby on you.
FLUTE
What is Thisby? a wandering knight?
QUINCE
It is the lady that Pyramus must love.
FLUTE
Nay, faith, let me not play a woman; I have a beard coming. (Act 1, Scene 2) 

The group decides to practice in secret so no one see their production (and no one will make fun of them).  In the play, the lovers talk to each other through a wall only.  The wall is played by an actor.  The entire story is explained in the prologue, which is Shakespeare’s way of poking fun at prologues that give away the ending.  Pyramus finds a shawl that has blood on it and thinks that Thisbe is dead, when in fact the lion did not maul her.  He kills himself, and then she kills herself.