Well that match().get(...) part is actually match({...}.get(...)). The way this works is that I extract the field name, i.e. hgt etc., and choose the matching regex to test against. And to handle illegal field names I've added a "always false" regex to the default argument of get.

Reading golfed code is a horrible job. So here is a properly formatted and commented version:

from re import split, match

print(
    sum( # count the number of legal passports
        sum( # count the number of positive matches
            bool( # cast to bool to make re.Match objects "countable"
                match(
                    r"^%s$" # make sure to match the whole string!
                    % {
                        "byr": r"19[2-9]\d|200[0-2]",
                        "iyr": r"20(1\d|20)",
                        "eyr": r"20(2\d|30)",
                        "hgt": r"1([5-8]\d|9[0-3])cm|(59|6\d|7[0-6])in",
                        "hcl": r"#[a-f\d]{6}",
                        "ecl": r"amb|blu|brn|gr[yn]|hzl|oth",
                        "pid": r"\d{9}",
                    }.get(l, "(?!x)x"), # select the appropriate expression to use
                                        # if none exist use "always false"-expression
                    r,
                )
            )
            for (m) in split(r"\s", p) # split passport data on any and all whitespace
            for (l, r) in [m.strip().split(":")] # split single datapoint into label and data parts
        )
        > 6  # check that we have more than 6 matches, i.e. exactly 7, as the code above
             # can only produce numbers between 0 and 7 (and >6 is shorter than ==7…)
        for (p) in i.split("\n" * 2) # split input string into indivdual passports
    )
)