The transformer is the low-current power supply for the control panel. The 110 VAC input is converted to a 16.5 VAC current limited output that can be ran on low-voltage wiring, 18 gauge speaker wire is recommended. The fused secondary is somewhat fragile, and the fuse cannot be replaced if blown. Luckily transformers are fairly cheap, a good replacement is available below.
Replacement Transformer at Amazon
18 Gauge Stranded Wire for Security Transformers