What is the vector table and what's special about its first entry?

The vector table is an array of 32-bit entries at the start of flash (by default) that the Cortex-M hardware uses to find exception and interrupt handlers, essentially a function-pointer dispatch table implemented in hardware. Most entries are handler addresses: the reset handler, NMI, HardFault, SysTick, then one per peripheral IRQ (EXTI, timers, UARTs, etc.), indexed by the NVIC when an interrupt fires. The special one is the first entry (offset 0): it is not a handler address but the initial stack pointer value, a data word the core loads into MSP at reset before executing any instruction, which is why the stack is valid from the very first cycle. The second entry is the reset handler. Two practical consequences: ISRs must have exactly the names the table expects (so the linker places them in the right slots, overriding the weak defaults), and in C++ handlers must be extern "C" to avoid name mangling so the table entry resolves, otherwise the interrupt vectors to a default infinite-loop handler and your ISR silently never runs.