The reference is to that loyal dog - Old Yeller - who turned rabid and had to be put down, much to Walter Brennan's heartbreak (wait - his song was "Old Rivers," never mind) and everyone in the audiences for that classic tear-jerking 1957 movie.
In tonight's Breaking Bad, Saul tells Walter that Jesse is like Old Yeller, a loyal dog of a partner who now has to be put down. Walter won't have Saul's metaphor or its suggestion to kill Jesse. But apropos the name and inevitable theme of the series, things now break from bad to worse.
Before the hour is over, Skylar - aptly being called Skeisenberg this season by many fans - is urging Walt to take care of Jesse - by which she clearly means and spells out, murder him. Hank doesn't give a damn about Jesse's survival either - it would be just fine with Hank if Walter kills Jesse in cold blood, as long as Hank has it on his recorder.
In the end, ironically, it's Jesse's unwarranted paranoia - unwarranted, in this case - that gets Walter to start the ball rolling on what he wants to be Jesse's death. Jesse wrongly thinks a tough guy - bald like Walter - was brought to their meeting by Walter to kill Jesse. Turns out he's just a guy waiting for his kid.
But in some ways the most powerfully heartbreaking moment in tonight's episode comes when Walter, Jr. says goodnight to his father by the pool in the hotel. First he hugs him. Then Walt tells Walt, Jr "I'll be up in a minute." And Walt Jr answers, "see you tomorrow."
Even Walt's loving son knows his father is lying - just about every time he opens his mouth. But Walt did cough tonight - which suggests he may be telling the truth about his recurring cancer being bad. Though, hey, I'm still hoping maybe he'll beat it after all.
See also: Breaking Bad Final Episodes #1: Walt vs. Hank ... Breaking Bad Final Episodes #2: Skylar and Jesse ... Breaking Bad Final Episodes #3: The Ultimate Lie
And see also Breaking Bad Season 5 Premiere: Riveting Entropy ... Breaking Bad 5.3: Deal with the Devil ... Breaking Bad 5.7: Exit Mike ... Breaking Bad Final Half-Season Finale
And see also My Prediction about Breaking Bad ... Breaking Bad Season 4 Debuts ... Breaking Bad 4.2: Gun and Question ... Breaking Bad 4.11: Tightening Vice ... Breaking Bad 4.12: King vs. King ... Breaking Bad Season 4 Finale: Deceptive Flowers