The most common format for storing e-mail messages on a hard drive is the mbox format, in which all the messages for each mailbox are stored as a single, long, text file. The mbox file identifies the start of each message by the "From" (sometimes "From_") line beginning each one. Taken in conjunction with an empty line, which signifies the end of the previous message, the word "From" at the start of a line indicates to a program the beginning of a new message.
Because a sender may include the combination of an empty line followed by a line starting with a capitalized "From" in the body of their message, an e-mail program searches the text of each message for this sequence and inserts > before the word "From" to indicate to the parser that, in this case, the word is simply part of the message. When this has happened, you may occasionally see ">From" starting a sentence in a message sent to you.