What's the difference between synchronous and asynchronous serial communication?

It's about how the receiver knows when to sample each bit. Synchronous communication has a dedicated clock line that the transmitter drives alongside the data; the receiver samples the data on each clock edge, so no prior rate agreement is needed and the link works at whatever speed the devices can follow, SPI and I2C are synchronous. Asynchronous communication has no clock line: both ends agree in advance on a bit rate (baud), and the receiver detects a start bit to mark the beginning of a frame, then samples at the agreed interval, recovering timing locally, UART is asynchronous. The tradeoff is a wire for a constraint: synchronous spends an extra pin on the clock but tolerates any speed and clock drift, while asynchronous saves the wire but demands both ends keep accurate, matched bit timing (typically within a few percent), or the sampling drifts off the bits and the data garbles.