One of the biggest misconceptions in fitness is you do no need to be big to be strong. But strengths not a product of the size of the muscle, it is a result of a neural impulse sent from the brain. If you are able to generate a larger electrical impulse to the muscle, there will be more muscle fibre recruitment. An increase in fibre recruitment will have a greater effect on increasing strength output than increasing the size of muscle fibres.
For you to hit that new PR, you have to believe you can lift the weight. You're lifting the heaviest weights with your mind, not so much with your body. The brain is made of neurons that send electrical signals to the body. This electrical signal travels through the peripheral nerves of the body to the muscle fibres that have been instructed to fire. If the peripheral nerves are not active, the corresponding muscle fibres will not be active either. If you want to be strong, focus on training your nervous system rather than the muscular system. Sure the muscles actually do the mechanical work, but they have to be signalled by the nerves.
No matter how big a muscle is, if the corresponding peripheral nerves are not active, it is useless. In other words, if you can flex a muscle harder, you are going to be able to generate more force. The ability to flex a muscle with more force comes from the electrical impulse the mind sends, not from the size of the muscle itself. So you could be really big and muscular, but very weak if your mind-muscle connection is not developed.
Also, if the muscular system is knotted up, flexibility will be compromised. You cannot be strong if you physically cannot get into the required positions for the lift. A new lifter will be very weak because they have not developed the flexibility the movements. For example, overhead press is a movement that requires full range of motion of the shoulder. A lifter who has never pressed above their head will not have the flexibility to do the movement properly under a heavy load. After a few weeks of developing shoulder mobility and training the movement pattern, the movement will suddenly become easy and pain free.
Another critical and often overlooked aspect of lifting heavy is timing. Having the muscles activate in the right order at the right time will increase your lifts significantly. This means studying the form of all the exercises you perform is critical for maximum gains. Taking videos of yourself and analysing your own form is a great way to improve form. Seeing exactly what you are doing form a third person perspective is very enlightening and beneficial.
The magic number of reps per set to build strength for most people is 5. Sets with 5 reps seem to be the right mix of power and volume for maximum neural stimulation. It is important to include very heavy triples, double and even singles if you truly want to be your strongest. This should be done relatively sparingly because it is extremely demanding on the nervous system.
Over taxing the nervous system will cause a decrease in performance over time. It is crucial to get enough rest in between heavy sessions so that the central nervous system is fully recharged and ready to fire. Heavy workouts focusing on the nervous system should only be done up to 3 times per week. Be sure to have at least one day off in between heavy sessions. A lighter volume workout is okay in between strength sessions, but these workouts should be more recovery focused.
So remember, believe you can lift the weight and you will. Study the proper form of exercises and compare it your own form. There are always tweaks to be made to improve strength performance. Finally, allow enough rest between heavy sessions for the nervous system to fully recharge and you will be stronger than ever!