The definitions of "second" and "metre" have not changed.
One second is defined in terms of frequency. Frequency is measured in hertz $(1\ \rm Hz=1\ s^{-1}$
We take an atom of $\rm Cs$. And then, we count the frequency of its spectrum. We extract the unit "1 second" from there.
As for the meter, we set that "one metre is the distance light travels in $\frac{1}{2,997955}~\rm s".$
So the meter and the second are perfectly defined.
The new thing is that the kilogram is no longer "the mass of a weight located in Paris, France". Now we have redefined it in terms of absolute things.
If you take the actual definition of metre and second, Plank's constant is
$$h=6,626\ldots \times 10^{34}~\rm Js$$
with many decimal numbers.
So we say "okay, let's cut the decimals somewehre". Let's say that Plank's constant is now EXACTLY
$$h:= 6.626 070 15 \times 10^{-34}~\rm Js$$
And then we say "adapt the value of $1~\rm kg$ so that Plank's constant is exactly that one.