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When (both are true) OR (both are false).
The idea is to get a simpler expression. If you need to build the hardware to implement a specific boolean expression, you can actually save money if the expression is simpler - and thus, you need less components.
Boolean logic can be thought of as "0 and 1" logic, or "True or False" logic. Boolean math started out as "True or False" expressions. In computers, the bits stored in memory are interpreted as either a '0' or a '1' (binary numbers). Computer scientists (usually, though you can prove out the concept either way) map '0' = FALSE and '1' = 'TRUE', and thus the operations and decisions made in a computer can be expressed/evaluated as Boolean logic/math expressions.
De Morgan's theorem is used to help simplify Boolean Expressions. Digital Circuits can be simplified by the application of this theorem.
Boolean algebra is a mathematical structure that deals with binary variables and logic operations. It is used to represent and manipulate logical expressions and truth values. Boolean algebra is especially important in computer science and digital logic design, where it is used for constructing circuits, Boolean functions, and making logical decisions.