Emily is Todd's ex-girlfriend who he had known since high school.
For an amount of time, Emily has wanted to get closer to Todd, whether it meant kissing or even having sex. While Todd seemed like he wanted to, he always felt reluctant, resulting in him striking out of every opportunity.
Emily though becomes more accepting of Todd. In the season 3 finale, when it becomes possible that Todd is asexual, Emily is very accepting of this and is willing to just remain good friends with Todd.
Emily is usually a very nice, friendly person overall, but can also seem to want a little more when it comes to relationships. She often is searching for something.
Todd Chavez: Close Friend
Bojack Horseman: Friend/One Night Stand