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“Unified field theory” is a slightly vague term that has been applied to various established and proposed theories. You’re presumably talking about one of three things. “Quantum field theory” is an approach to quantum mechanics that was developed from roughly the 1920s to the 1970s and turned out to be an extremely good way of describing particle physics. Within this framework, electromagnetism and the weak nuclear force have been pretty much fully understood. However, the strong nuclear force, which is the main thing that holds atoms together, is much more complicated. A “grand unified theory” would fully describe the strong force in combination with those other two forces. A “theory of everything” would also include gravity.
The main reason for wanting to develop theories that include all these forces is that there are processes that involve all these forces and presumably cannot be fully understood by considering them separately.
Also, historically, it has generally been very fruitful for physicists to combine disparate observations into unified theories. For example, in the 19th century people kept developing all kinds of new ideas about electricity, magnetism, and what we now know as electromagnetic radiation (light, radio waves, etc.). Various connections between these ideas were noticed, and eventually a unified theory of classical electromagnetism was developed that united them all and improved our understanding of all of them individually.
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