The siege flags are flown from the walls on the anniversaries of both the Shutting of the Gates, and Relief of Derry at the beginning and end of the siege respectfully.
The Cross of St George on the left and Green Ensign on the right were the flags used in Ireland on land and at sea at the time of the siege. St George's Cross being used on Garrisons like Londonderry and the Green Ensign used on Irish ships although it is debated if this flag had any official status, there is evidence it was used none the less.
The flag in the centre is known as the Crimson Banner and it was first hoisted on the walls and later St Columb's Cathedral by the cities Governor Colonel Mitchelburne as a symbol of defiance or distress or possibly to boost moral, depending on who you talk to. Local legend says the crimson colour comes from the flag being stained by the blood of the city's defenders although sources differ on what the original flag was, some say it was a rag dipped in blood one says it was an unused maritime ensign stained with blood. Col Mitchelburne founded the forerunner of the Apprentice Boys Clubs in 1714 and left money in his will to hoist his Crimson flag from the Cathedral on the anniversaries of the beginning and end of the siege, which continues today. As well as the walls and Cathedral the crimson flag is flown from the Apprentice Boys Memorial Hall, and versions are carried by Apprentice Boys clubs on parade.
For more information on the city walls, the siege, or the commemorations you can visit:
Associated Clubs of the Apprentice Boys of Derry Website
Derry's Walls Website
Siege Hero's Trail
Or various documentaries about the siege on YouTube
BBC "The Siege"
BBC "Battle Field Britain" Clip
Museum audio-visual displays: One, Two and Three.