It can work a couple ways. One version is called a “capacitive sensor.” These sensors detect the electric charge when you place your thumb on them. As a general rule, the ridges of your fingerprint should cause a charge, while the valley would cause less to no charge. This makes intuitive sense; if I placed my fingertips on a hot burner, my palm would feel less heat because it’s not directly touching the heat (or it’s touching the heat a little less). From that information, the sensor can determine your fingerprint.
Another option for phones is ultrasonic. This sends ultrasonic sound waves at your finger and measures what bounces back. Depending on the pattern, the sensor can determine your fingerprint. It’s a lot like echolocation in bats.
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