They seem very strange now with peculiar values but wind the clock back over 50 years and the pre-decimal system was not only used in Great Britain but also Ireland, Australia, New Zealand South Africa and the Caribbean. These all went decimal in a period from 1960 for South Africa to 1971 for Great Britian.
The big advantage of the pre-decimal system is its ease of division with lots of ways of dividing the 240 pence in each pound. The decimal pound of 100 pence has many fewer ways of being split.
The decimal pound is easier when multipling up as it is all in 10s while the old pound was 12s for pennies and 20s for shillings.
These are the pre-decimal coins
Farthing - This was a quarter of a penny so there were 960 in a pound and was last issued in 1956.
Half Penny - There were 480 in a pound or 24 in a shilling.
Penny - A large bronze coin and there were 240 in a pound or 12 in a shilling.
3 Pence - A brass coin issued from 1937 to 1967 and there were 4 in a shilling.
6 Pence - There were 2 in a shilling or 40 in a pound and equal to 2.5 pence in decimal.
Shilling - There were 20 in a pound and equal to 5 pence in decimal.
Florin or 2 shillings - There were 10 of these to the pound so equal to 10 pence decimal.
Half Crown - These were equal to 2 shillings and 6 Pence and there were 8 in pound.
Crown - These were 5 shillings but were only issued to celebrate special occasions (coronations etc).
Despite decimal day being nearly 50 years ago these are still all redeemable at Foreign Money Exchange.