It's usually not much of an issue, but sometimes it can be a problem you need to be aware of. Most decent clients seems to pick a reasonable setting by default.
The problem is mostly the diffence in the end of line (EOL) charcter between Unix and Windows. (Or other systems). On Unix, I believe it's only charcter 10 (Line Feed), but on Windows, and EOL is two characters 13, 10 (Carriage Return, and Line Feed).
The setting is basically so it can translate the end of line charcter between the two systems during transfer. It's often not a big problem with text files, since many utilities now support either way to end a line without major issues. However, a lot of text editors will still display funny results. On Unit, with a Windows text file, you'll see a lot of "^M" at line breaks, which is the other character which some Unix editors don't know what to do with. On Windows with a Unix file, you might get everything all on one line as it can't find a full EOL, and so keeps going on the same line.
But like I said, a lot of programs will be able to handle both. Some won't though. It's usually fairly safe to transfer a text file in any mode. Even if you get funny output, it's a simple matter to run the file through an automated converter to fix it. (I think many Unix systems have something called dos2unix, and unix2dos, or maybe just d2u, and u2d. They do seem to be overly fond of excessive abbreviations).
The problem is a lot more serious for binary files though. If you send a binary file through text mode, then it can convert the bytes it preceives as EOL characters, and corrupt the file. Binary mode is basically just a direct byte copy without conversion, so it won't corrupt anything or change anything it's not supposed to. (It won't convert your text files for you). If in doubt, binary is the way to go, and seems to be the default of most modern FTP cilents. Some of them will look at the first few bytes of a file though to see if it's ASCII text, and use ASCII mode on you automatically. This can be a problem if you have a binary file that starts with ASCII text, causing some clients to use the wrong mode and corrupt your file.