You, the reader, are not expanding, even though the Universe in which
you live is.  There are two ways to understand this.

The simple way to understand the reason you're not expanding is that
you are held together by electromagnetic forces.  These
electromagnetic forces are strong enough to overpower the expansion of
the Universe.  So you do not expand.  Similarly, the Earth is held
together by a combination of electromagnetic and gravitational forces,
which again are strong enough to overpower the Universe's expansion.
On even larger scales---those of the Solar System, the Milky Way, even
the Local Supercluster of galaxies (also known as the Virgo
Supercluster)---gravity alone is still strong enough hold these
objects together and prevent the expansion.  Only on the very largest
scales does gravity become weak enough that the expansion can win
(though, if there's enough gravity in the Universe, the expansion will
eventually be halted).

A second way to understand this is to appreciate the assumption of
homogeneity.  A key assumption of the Big Bang is that the Universe is
homogeneous or relatively uniform.  Only on large enough scales will
the Universe be sufficiently uniform that the expansion occurs.  You,
the reader, are clearly not uniform---inside your body the density is
about that of water, outside is air.  Similarly, the Earth and its
surroundings are not of uniform density, nor for the Solar System or
the Milky Way.

This latter way of looking at the expansion of the Universe is similar
to common assumptions in modelling air or water (or other fluids).  In
order to describe air flowing over an airplane wing or water flowing
through a pipe, it is generally not necessary to consider air or water
to consist of molecules.  Of course, on very small scales, this
assumption breaks down, and one must consider air or water to consist
of molecules.  In a similar manner, galaxies are often described as
the "atoms" of the Universe---on small scales, they are important, but
to describe the Universe as a whole, it is not necessary to consider
it as being composed of galaxies.

Also note that the definitions of length and time are not changing in
the standard model.  The second is still 9192631770 cycles of a Cesium
atomic clock and the meter is still the distance light travels in
9192631770/299792458 cycles of a Cesium atomic clock.