Last weekend was the 2014 NFL Scouting Combine in Indianapolis at Lucas Oil Stadium. During that time scouts are able to watch players go through their workouts as well as interview as many as 60 players they may be interested in for 15 minutes. Here are some players that interviewed with the Rams.
UCF-QB Blake Bortles via Paul Tenoria of the Orlando Sentenial
A&M-OT Jake Matthews via TurfShowTimes
Ptt DT Aaron Donald via TurfShowTimes
Lindenwood WR Pierr Desir via Jim Thomas Twitter Account
Okla St.- CB Justin Gilbert via Jim Thomas Twitter
Lou- S Calvin Pryor via Jim Thomas Twitter
TCU- CB Jason Verrett via Jim Thomas Twitter
Mizzou- CB E.J. Gaines via Jim Thomas Twitter
Alabma- S Ha Ha Clinton Dix via Jim Thomas Twitter
Clemson- WR Sammy Watkins via Nick Wagoner Twitter
Auburn- OT Greg Robinson via Brandon Marcello Huntsville Times
Auburn- RB Tre Mason via Chris Perkins SunSentinal
*The Rams also met with Clowney in Rock Hill South Carolina via Yard Barker and NFL insider Ian Rapoport.
These are all the players from different sources that I could find that said the Rams had interviewed a particular player, however with the Rams being able to interview 60 players, they probably interviewed 60 players.
Teams interview players for many reasons, whether it be to just do research on the player or that they are actually interested in the player. Teams will also have the chance to bring in players for private workouts as the draft approaches.