Did you try the man page for ksh? (man ksh) The man page has the info that you are looking for. If you have additional questions, after reading the specific areas in the man page, one of us can help.
The specific section you're interested in is "parameter expansion". You should find it documented in the man page of any shell that supports those idioms.
Mask a regular expression, taking the less greedy portion, starting from left to right.
e.i.
Match as less as possible, zero or more characters, followed by a literal '1'
In your case if x="a1 b1 c2 d2" it matches 'a','1' and stops, returning the remainder as the result. "b1 c2 d2"
Mask a regular expression taking the most greedy portion starting from left to right
e.i
${x##*1} -> match as much as it can. Returns remainder.
if x="a1 b1 c2 d2" then it eats 'a','1',' ','b','1' and stops.
Start from right to left matching as less as possible.
Start from right to left matching as much as possible
Match a literal '1' followed by zero or more characters. (translates to nothing or everything else after a '1' included)
Match zero or more characters followed by a literal '1'. (Translates to everything before a literal '1' or nothing plus '1')