Furnace turns on but blower will not work. I was told it is the transformer. Could it be and what does it do?

The transformer provides power to relays or contactors, to engage the Big power(blower). That way thermostat does not need very large wires. (relatively speaking)

A bad transformer and nothing happens except some furnaces default to the blower running.

Go to the sticky at https://www.askmehelpdesk.com/heating-air-conditioning/heating-cooling-maintenance-repair-troubleshooting-frequently-asked-questions-58313.html
Follow the sequence of operations and see where it stops. Try to figure out the code is it has a red blinking light.

Likely who told you it was bad, measured primary voltage in, voltage was present, and there was no low voltage out. Less than $20 part.
Primary, and secondary voltages need to match existing. And the Volt/Amp rating should match or exceed existing transformer.