tkamiya is quite right...
Imagine you have one of those inverters that change 12VDC from your car battery to 120VAC to run a small TV. The package contains a circuit called an oscilator to convert DC to AC. That is coupled to a transformer to step up the voltage. It also contains other components to smooth out the voltage so your TV for example will not have a mess of interference on the screen and buzzing in the audio.
Any electronic flash does the same thing except it generates a much higher voltage in the order of hundreds of volts! The circuit does a couple more neat tricks. The high voltage is converted back to a high DC voltage again and charges up the "main capacitor." The main capacitor is connected to switches, (the test switch) and your sync connector. When either of these contacts close, the mail capacitor dumps its high voltage charge through a pulse transformer that results in THOUSANDS of volts to cause your flash tube to arc and give you the flash for your photo.
The trouble in your flash could be a transistor, coil, transformer, capacitor or many other components. It could be as simple as the on/off switch corroded.
Please leave the troubleshooting to an experienced tech or at least make sure the battery is disconnected AND any charge on the capacitor is discharged.