The most important difference to be aware of is that with a stream opened in text mode you get newline translation on non-*nix systems (it's also used for network communications, but this isn't supported by the standard library). In *nix newline is just ASCII linefeed, \n, both for internal and external representation of text. In Windows the external representation often uses a carriage return + linefeed pair, "CRLF" (ASCII codes 13 and 10), which is converted to a single \n on input, and conversely on output.
From the C99 standard (the N869 draft document), §7.19.2/2,
A text stream is an ordered sequence of characters composed into lines, each line
consisting of zero or more characters plus a terminating new-line character. Whether the
last line requires a terminating new-line character is implementation-defined. Characters
may have to be added, altered, or deleted on input and output to conform to differing
conventions for representing text in the host environment. Thus, there need not be a one-
to-one correspondence between the characters in a stream and those in the external
representation. Data read in from a text stream will necessarily compare equal to the data
that were earlier written out to that stream only if: the data consist only of printing
characters and the control characters horizontal tab and new-line; no new-line character is
immediately preceded by space characters; and the last character is a new-line character.
Whether space characters that are written out immediately before a new-line character
appear when read in is implementation-defined.
And in §7.19.3/2
Binary files are not truncated, except as defined in 7.19.5.3. Whether a write on a text
stream causes the associated file to be truncated beyond that point is implementation-
defined.
About use of fseek, in §7.19.9.2/4:
For a text stream, either offset shall be zero, or offset shall be a value returned by
an earlier successful call to the ftell function on a stream associated with the same file and whence shall be SEEK_SET.
About use of ftell, in §17.19.9.4:
The ftell function obtains the current value of the file position indicator for the stream pointed to by stream. For a binary stream, the value is the number of characters from the beginning of the file. For a text stream, its file position indicator contains unspecified information, usable by the fseek function for returning the file position indicator for the stream to its position at the time of the ftell call; the difference between two such return values is not necessarily a meaningful measure of the number of characters written or read.
I think that’s the most important, but there are some more details.
