The base of the all is to match the first four characters in a line (the four dots) and put tem into a variable (the surrounding escaped brackets), then match the 6th and all following characters and put them into a variable too - in other words, match the complete line except the fifth character. I have marked the first, second and third part of the regexp with 1, 2 and 3 for you. In the output you skip part 2:
sed 's/^\(....\).\(.*\)$/\1\2/'
111111112333333
The other sed-statement is just a variation on that. You can "multiply" regular expressions: The asterisk is such a "multiplier", it will create a copy of the previous regular expression as often as it is needed to match. The construction with the curly brackets is less vague: you can control the exact number of repetitions or even a range of repetitions. The following regexp parts are examples of this:
/..../ /.\{4\}/ -> four times the preceding "."
/.*/ -> matches 0 or more instances of "."
/.\{4,5\}/ -> matches 4 or 5 instances of "."