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
offsetshall be zero, oroffsetshall be a value returned by an earlier successful call to theftellfunction on a stream associated with the same file andwhenceshall beSEEK_SET.
About use of ftell, in §17.19.9.4:
The
ftellfunction obtains the current value of the file position indicator for the stream pointed to bystream. 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 thefseekfunction for returning the file position indicator for the stream to its position at the time of theftellcall; 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.