Basically, ./ is the current directory, while ../ is the parent of the current directory. Both are actually hard links in filesystems, i.e., they are needed in order to specify relative paths.
Let's consider the following:
/root/
directory_a
directory_a_a
file_name
directory_a_b
file_name
directory_b
directory_b_a
directory_b_b
and let's consider your current working directory is /root/directory_a/directory_a_a. Then, from this directory if you refer to ./file_name you are referring to /root/directory_a/directory_a_a/file_name. On the other hand, if you refer to ../file_name you are referring to /root/directory_a/file_name.
In the end, ./ and ../ depend upon your current working directory. If you want to be very specific you should use an absolute path.