Nicholas Copernicus, a Polish scientist living about a century
before Galileo, had already come up with the unorthodox idea that
the Sun was at the center of the solar system. Galileo knew about
and had accepted Copernicus's heliocentric (Sun-centered) theory.
It was Galileo's observations of Venus that proved the theory.
Using his telescope, Galileo found that Venus went through phases,
just like our Moon. But, the nature of these phases could only
be explained by Venus going around the Sun, not the Earth. Galileo
concluded that Venus must travel around the Sun, passing at times
behind and beyond it, rather than revolving directly around the
Galileo's observations of the phases of Venus virtually proved
that the Earth was not the center of the universe. It was this
assertion which most angered the Church leaders of the time.
To experiment for yourself with how Galileo used phases of Venus to prove a heliocentric solar system, try
Proving a Sun-centered Solar System