How the numbers work
Each digit is the sum of read (4), write (2) and execute (1). The first digit is the owner, the second the group and the third everyone else, so 7 is 4+2+1 for full access, 5 is read and execute and 4 is read only. 755 means the owner can do everything and others can read and run. On a folder, execute means being allowed to open it and reach the files inside.
Setuid, setgid and sticky
An optional fourth digit at the front adds special bits: 4 for setuid, so a program runs as its owner; 2 for setgid, so it runs as its group, or on a folder new files inherit the folder's group; and 1 for sticky, so in a shared folder like /tmp people can only delete their own files. In the letters form they show as s or t in place of x, and as a capital S or T when execute is off.
Changing permissions with letters
The Apply a change box understands chmod's own syntax. Pick who with u, g, o or a, then + to add, - to remove or = to set exactly, then r, w and x. u+x makes a script runnable, go-w stops others writing, and a+X adds execute only to folders and files that already have it. Separate several changes with commas.