The person saying that they will bet a penny to a pound, means that they are completely sure that they are correct, and therefore would win the pound for the small outlay of a penny.
Just realised, it also works the other way around, i.e to bet a pound to a penny, meaning they are so sure they are correct that they have no chance of losing the pound.
Don't want to be thought pedantic, but this saying was around before we went decimal. So the odds would be 240 to 1. (12 pennies to a shilling, and 20 shillings to a pound).