What are "conflicts" and why do firms run them?
In a very tiny nutshell*, conflicts rules dictate that a lawyer can’t represent a client whose interests are adverse to a current client or former client.
Law firms can have a lot of lawyers, and conflicts rules apply to each and every one of them. That's a lot of potential conflicts, and a lot of ways to get in trouble.
So, any time a firm brings in a new attorney, the firm needs to run that attorney's potential conflicts against aaaallll the other potential conflicts at the firm. If there's a hit, the firm needs to investigate whether it's a conflict that a current or former client could, or would, waive. More often than not, because it's a small world, a conflict flag does go up, but it's waived before the new hire ever knows about it. Occasionally though, a big enough conflict arises that the firm can't hire the new person. Which sucks.
*In a slightly bigger nutshell, the ABA Model Rules of Professional Conduct state:
[A] lawyer shall not represent a client if the representation involves a concurrent conflict of interest. A concurrent conflict of interest exists if:
(1) the representation of one client will be directly adverse to another client; or
(2) there is a significant risk that the representation of one or more clients will be materially limited by the lawyer's responsibilities to another client, a former client or a third person or by a personal interest of the lawyer.