I will use several Arduino boards that are connected to each sensor.
Press the push button to start outputting sensor data.
I have to start multiple boards at the same time, but is it possible with a push button?
For example, five Arduino boards are connected to a push button, and when the push button is pressed, can a HIGH signal be output to each board?
Thank you.
Yes, as well as a negative signal.
Please post a drawing showing the intended setup. Pen and paper would work.
How many boards and how far apart from each other are they?
Use one button. Use one resistor wired as a pullup resistor. Route one switch pin to ground and the other to the pullup. The other end of the pullup goes to 5 volts or Vcc, and the pulled up switch contact can be fed to all the Arduino inputs up to way more than you have I am guessing.
The pullup value isn't terribly critical, anything like 4K7 or 10K would be fine.
Obvsly, I hope, the action would be launched when each Arduino sees that pin go LOW, button presst.
So the only thing to worry about is if they are all over the place physically, in which case a little more care might need be taken.
a7
And the elephant question: 
Why would you use more than one Arduino module? 