The Resend Button is an extension, that allows you to quickly resend all local trains that are currently on your main station, with one single button, to the same destination that they where sent to before.
The Resend Button can be purchased in the Station Themes and Extensions tab in the shop.
To use it, you have to first manually send the train to the desired destination. After the train arrives back on your station, the resed button will appear in the right side of the screen on the main station, as shown here:

You may also use the button in the Train Manager, which looks like this.

The Resend button works also for IT trains in the same way. You have to first send the train to a contractor, and when it arrives back in your station, you can send it with one button to the same contractor again. This is done in the Train Manager only, since your own IT trains are not visible in your station.
Keep in mind that this button may not appear, when using the special 20 minute train ride once it expires. This is due to the destination not being avaliable, hence you have to set up a different destination manually, or wait till it activates again. This is the same case with special event destinations, as once they are removed or not avaliable anymore, you need to set up a new destination by hand. After that you may however again use the Resend button.