'Rep' is short for reputation.
Its similar to the "Like" button. If you like or agree with something someone said, you hit the 'rep' button.
The difference between "Like" and "Rep" is that while the "Like" is specific to a particular comment, the "Rep" adds points to the user's cumulative Reputation score.
A person with a high reputation score is a member that has been judged by the community as someone who offers insightful contributions and brings value to the forum and it's dialogue.
Depending on how the system is set up, a person's ability to increase another member's reputation can be based on several factors including the user's own reputation score, post count and join date. Calboner, for example, being a more senior member, could increase someone's reputation more than I could. It's a system to give a bit more weight to the opinions/judgement of more senior and highly respected members.
Here's an example of the 'rep' system in use:
Streetcar systems in planning (sales, 2011, neighborhood, construction) - Urban, city, town planning, land use, zoning, transportation and transit, environmental issues, urban design, community development, subdivisions, revitalization - City-Data Fo
On the top right side of each post, you'll see a summary of the user info along with a reputation score.