At startup, the capacitor will be discharged. When power is first applied, the capacitor holds the reset signal low for a short period of time while it charges. This is a very common approach to power-on reset.
We know that the time constant Tau=R*C is 1 ms and in that time the voltage on the capacitor will charge to 63% of Vcc. Without doing the math, it is likely that the signal will be below the logic '1' threshold for, perhaps, 500 us. Maybe a little less, maybe a little more, it depends on the threshold voltage.
R is in Ohms, C is in Farads so Tau = (1 * 104) * (1 * 10-7) = 1 * 10-3 = 1 ms
We also know the charging equation
Vout = Vin * (1-e-t/Tau) and it turns out that at t = 1 Tau the output is 63% of the input.