The execution thread that wants to signal the completion of the intended task calls complete() to a waiting thread so that it can continue. Threads will be awakened in the same order in which they were queued. In the case of multiple waiters, it calls complete_all():

void complete(struct completion *x)
{
        unsigned long flags;

        spin_lock_irqsave(&x->wait.lock, flags);
        if (x->done != UINT_MAX)
                x->done++;
        __wake_up_locked(&x->wait, TASK_NORMAL, 1);
        spin_unlock_irqrestore(&x->wait.lock, flags);
}
EXPORT_SYMBOL(complete);
void complete_all(struct completion *x)
{
        unsigned long flags;

        spin_lock_irqsave(&x->wait.lock, flags);
        x->done = UINT_MAX;
        __wake_up_locked(&x->wait, TASK_NORMAL, 0);
        spin_unlock_irqrestore(&x->wait.lock, flags);
}
EXPORT_SYMBOL(complete_all);