Modified from an earlier answer (OP was asking about the royal flag):

The three gold lions on a red field on either royal standard are the symbols of the former Kingdom of England, which existed from about the mid-10th century to 1707, when England merged with Scotland to form the nation of Great Britain. The three lions date back to the personal arms of Richard I, and have been used in various heraldic combinations with other arms over time (e.g. Edward III combined them with the fleur-de-lis to press his claim to France).

The lion of Scotland dates back to William I, and is similarly a symbol of the Scottish kingdom which ceased to exist in 1707.

Now, as to "why lions," the use of the lion as a heraldic symbol dates back to the very earliest Middle Ages. There are a bunch of previous posts on this (I'm stealing the formatting from a post from u/searocksandtrees):

• Why are lions so prominent in the history of Europe? - /u/JoshoBrouwers discusses the symbolism of lions, and their former range

• How common were wild lions in ancient Greece? - /u/plinythehipster talks more about their range and mentions in Greek lit. There's more from pliny in Why is England's national animal the lion even though lions are not native to the area?

• When did lions (cave or otherwise) die out in Italy? - featuring /u/Gargatua13013 and /u/Mulberry_mouse

• Did Europeans in the early and the high middle ages tame and import lions to Europe and Britain? - lions as prestige items (gifts, possessions)

• How come the lion is part of the coat of arms for so many northern European countries (Sweden, Norway, Finland, Scotland, UK, Denmark) despite lions living exclusively in Africa? - more on prestige, and heraldry

• Maned lions are ubiquitous in English iconography, heraldry and lore. Given that the last of the European lions died out in Greece around 100 BCE, this seems strange. Did lions take on a more mythical character than biological reality in medieval British minds? - more prestige

In terms of lions existing in England, there were lions in the Tower of London for several centuries, though probably not continuously -- King John founded a royal menagerie sometime around 1200, and lion skulls found in the tower's moat date to as far back as 1280 or so.