How do people manage the constant pressure that is put on them to succeed?
I am assuming you want to know how people successfully manage this pressure. It is important for a person to know themselves—what is important to them, what they are drawn to, what they are good at—and to let that be their guide, rather than the expectations of others. The psychobabble terms for external pressure vs. internal pressure are External Locus of Control and Internal Locus of Control. These terms refer to what factors are most important for motivating and evaluating the success of our behavior. Those with an External Locus of Control are worried about what others value and what others think. Those with an Internal Locus of Control are guided by their own values and thoughts. It is hard to have an Internal Locus of Control when we are young, and, for many, when we are older, too. However, many develop more and more ability to be their own guides as they gain more life experience. People are happier when they are their own guides.
This fits well with the Christian life, too. Jesus did not seem concerned about externals, and, in fact, spoke most strongly against the Pharisees, who looked very faithful but whose internal motivations he knew were not positive. When we are focused on being who God wants us to be, then the external pressures become less significant.