RIR is a tool for picking the weight you will use for a given exercise. RIR, or "reps in reserve," is a type of system coaches refer to as "autoregulation." This is a fancy word that basically means a given weight feels heavier on some days than it does on others depending on the many factors that contribute to recovery and readiness for training. Using an autoregulation system like RIR (or RPE, rate of perceived exertion), allows an athlete to adjust load intensity to accommodate for fluctuations in stress, fatigue, nutrition, mood, hormones, soreness, etc. In its most basic definition, an RIR 4 means that you *could* do 4 more repetitions beyond the end of the prescribed set -- and no more than 4 additional reps. In a program, it often looks like this: 1 set of 5 reps @ RIR 4 This would translate to loading the bar with your 9RM (9-rep max) or a weight you could ONLY execute for exactly 9 reps while the last few reps are a slow grind. This does not mean you will actually perform 9 reps, you will only perform 5 and keep 4 reps "in reserve" or "in the tank," so-to-speak.
It's difficult to get good at rating RIR and requires time and practice to do so accurately. Beginners tend to severely overshoot or undershoot RIR so if you're just starting out, it's good rule of thumb to stick with an RIR 4-5: we would expect the bar speed to stay consistent throughout the end of the set rather than slowing down on the final rep or last two reps.