The Cold Open is the part of a television program that occurs after the end of the preceding program and before the title card and/or opening credit sequence. The 'Cold' part comes from the fact that viewers watching them after the end of whatever program they were watching before are coming to the show with absolutely no information about what it is that they're looking at. Those first few seconds more or less determine if the show gets new viewers or not.
On a thematic level, a Cold Open serves to drop viewers straight into the action without having them watch a title sequence. It's an effective way to give a story a running start, and it establishes the pacing for the rest of the program.
Cold Opens used to be less common occurrences than they are now, restricted to hour-long dramas that asked a more substantial investment of a viewer's attention. Nowadays you see them everywhere, and their proliferation has muted their effect somewhat.