TTL is an old digital logic family. A "TTL to RS232" cable is a voltage level converter. Some electronic devices have a serial connection that is in RS232 format, but with voltage levels of 0 to 5V or less, while the RS-232 levels are a minimum of +/-5V, maximum of +/-15V. The "TTL to RS-232" cable boosts the TTL or 0-5V logic levels up to the higher voltages required by the RS-232 standard. These typically use the MAX232 integrated circuit from Maxim Integrated Products.
Although not guaranteed, the serial ports on most computers will will respond to TTL levels or 0-5V logic levels.
Serial ports, even those with TTL or CMOS logic levels rather than the true RS-232 voltage levels are designed to withstand being shorted out or having 12V applied. So it is relatively safe just to hook up what cables you have and see if they work.
Charlie