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When dealing with integrals, it's important to understand that evaluation refers to the process of finding the numerical value of the integral. In this exercise, we were tasked with evaluating a triple integral, which involves calculating an integral in three distinct stages with each stage corresponding to one of the variables: \(x\), \(z\), and \(y\).

We started with the innermost integral, \(\int_{0}^{1} y z e^{x} d x\), integrating first with respect to \(x\). This required using the exponential integration rule that simplifies to \(e^{x}\) evaluated between 0 and 1. This calculation reduced our expression to \(yz(e - 1)\).

The next step was evaluating the integral with respect to \(z\). Again, we applied the limits given from 1 to 2. Finally, the outermost integral, with respect to \(y\), used similar techniques. As you move from the innermost to the outermost integrals, keep substituting back from the calculated expressions to always refine the integral and maintain integration bounds. The ultimate goal is to simplify the function entirely and arrive at a numerical value.

When evaluating multiple integrals, especially in calculus, it is common to perform what is known as iterated integration. This involves evaluating each integral one at a time, starting with the innermost integral and moving systematically outward.

In our triple integral scenario, the process was to first evaluate the integral with respect to \(x\) while treating \(y\) and \(z\) as constants. Subsequently, we worked on the resulting expression for \(z\), treating \(y\) as constant. Lastly, \(y\) integration was executed which concluded the iterated integration process. This step-by-step approach helps manage complex problems and streamline the calculation process to support deep understanding of how each part contributes to the final answer.

Iterated integrals encapsulate a strategy of reducing multidimensional integration problems by breaking them down into stepwise single-variable problems, simplifying the computational challenge that continuous integrals can pose.

Understanding integration techniques is crucial when tackling problems like this. Knowing when and how to apply specific rules and formulas can make the task of integrating more manageable.

In this problem, the primary technique used is the substitution rule for the exponential function, where we integrated \(e^{x}\) between certain limits. It's vital to be familiar with common integrals, such as those of exponential, logarithmic, and polynomial functions, and how to use these to simplify expressions.

Another technique is recognizing that constants can be factored out of the integral to simplify the process, which we see in evaluating \(yz(e-1)\) while integrating with respect to \(x\). Further, careful selection of the order of integration can simplify the problem significantly, especially in cases of complex or non-standard regions of integration. Choosing wisely can result in simpler bounds or reduce complexity, as was exemplified in the conclusion of this triple integration task where the expression could be simplified to a straightforward arithmetic computation.