Yes it's safe to eat an avocado that has turned brown.
The avocado turns brown just like apples do when exposed to the air and It's caused by a chemical reaction called oxidation and does not mean that the avocado is bad.
The avocado may just be bitter tasting and doesn't look good but the brown avocado is still very safe to eat as long as it hasn't grown any mold or other bacteria on it.
Opened Guacamole will sometimes turn brown as well on the top and it's still very safe to eat although it might also have a bit of a bitter taste to it.
It's just that chemical reaction that happens when it's exposed to the air but it's nothing that will make you sick.