A system is causal when its output at a given time depends only on present and past input values, never on future input values.

A memoryless system uses only the input at the same instant. For example,

$$y(t)=x(t)^2$$

is memoryless, while

$$y(t)=x(t-1)$$

has memory because the output depends on an earlier input value.

A system is bounded-input bounded-output stable, or BIBO stable, when every bounded input produces a bounded output. If

$$|x(t)|\le M_x<\infty,$$

then stability requires some finite $M_y$ such that

$$|y(t)|\le M_y$$

for the resulting output.

Causality asks whether a system can operate without knowing the future. Memory asks which input times matter. BIBO stability asks whether finite-amplitude inputs can generate unbounded outputs. These are independent properties and should be checked separately.