The 555 (when wired as a monostable) triggers (OUTPUT goes high, and timing starts) during the down-going edge of the TRIGGER. To get the PERIOD T implied by R*C, the TRIGGER pulse must be shorter than T. If TRIGGER is longer than T, then T lasts until TRIGGER goes back high beyond its natural timing interval.
The TRIGGER input usually has a DC blocking (coupling) capacitor with a resistor pull-up to make it truly "edge triggered" instead of "level triggered".