19-year cycle

I have heard every 19 years (235 lunar months) the moon and the solar
year are synchronised. However, after looking at the times for new
moons in the almanacs, and comparing new moon times with a year and a
year 19 years later, the new moon can be off as much as one day. March
16 in the first year and March 15 in the 20th, which is 19 years later.
Why is this? Is there any truth to the 19-year cyle?