You should download & review the manual for Amtrol Boilermate products here
Page 12 of the manual begins examples of wiring between the Boilermate and aquastat (also gas valve and multi-zone relay), that is usually mounted on the boiler. In order to use it correctly, you'll need to determine which aquastat (or other device) your furnace has. You should be able to locate this info on the inside of the aquastat cover. The Honeywell Triple Acting aquastat is very common and looks like this:
The cover is held by a single screw on the top, bottom or front (depending on the model you have). The inside should have wiring information along with the model number. Compare the model number with the wiring diagram for it in the Boilermate manual.
Make sure power is OFF before continuing.
Check that all wires are terminated and undamaged. Make sure terminal screws are not loose. Tighten any found to be loose.
The orange wires are connected to a switch that is normally OPEN but CLOSES to start the boiler when the hot water has cooled. It is also used to operate a "power vent" for a minute or two both before ignition and after flame out for safe pre and post purging of the combustion chamber of furnaces that lack a chimney.
Blue wires are connected to a switch that is also normally OPEN but CLOSES to start the boiler when the hot water has cooled. When the switch connected to these wires is CLOSED, ignition happens instantly. There is no delay for purge so when these wires are used to start a furnace, it should be one with a chimney - not a power vent.
For additional help with your particular installation, you will need to provide information concerning the wiring diagram in the manual that applies. Otherwise, there are simply too many variations to walk through.
I suspect that the switch(es) that are connected to the orange (or blue) wires - or the device (aquastat or multi-zone relay box) is not operating as expected to start the furnace.
The troubleshooting section of the manual that seems to apply best is the section: Boiler will not operate when calling for hot water
on page 27 (if you want to try some of their suggestions while waiting for additional replies).
I hope this helps..