In any equation of any kind, a value "satisfies" the equation when it makes the equation a true statement after being substituted for the variable.
If you put the coordinates of a point into either the vector equation or the parametric equations, those equations will be "satisfied" if they become true statements after the substitution.
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Trivial example:
.. x = 2
is "satisfied" by x having the value 2, because
.. 2 = 2
is a true statement.