A value of x that determines f(x)=g(x) means that for said value of x, f(x) and g(x) will have the same value. This is the point (or points, depending on the form of the functions) where both functions intercept.
Looking at the table you can see that
For x=-1
f(x)=1
g(x)=1
Is the only value of x where both functions have the same value.