The term phenomenology means the study of phenomena, where phenomena means observable experience. The chief difference between phenomenology and empiricism (which also studies observable experience) is that phenomenology tends to focus on subjective, first-person experiences of the world, whereas empiricism aspires to create an objective, third-person experience of the world.
The “existence” in Existentialism, on the other hand, comes from the idea that “existence precedes essence,” where an object’s essence is viewed as a set of indispensable defining characteristics common to all such objects. A chair, essentially speaking, is a four-legged object that people sit upon; a mirror is essentially an object that casts a reflection. The existentialist claim is that human beings have no such essence. We, as human beings, create our own self-definitions through freely willed actions. We cannot be predefined, our essences are not predetermined, but created in each new moment through the acts that compose our existence.
What the two movements have in common is a radical emphasis on the first-person perspective, which helped the Phenomenology of thinkers such as Heidegger and Husserl to become a major influence on the familiar French Existentialism of Sartre and Camus. Rather than saying that the two philosophies synthesize well with each other, therefore, it might be more accurate to say that the most familiar form of existentialism is itself a synthesis of the first-person perspective of phenomenology with the will-driven radical freedom of thinkers such as Kierkegaard and Nietzsche.