Let's say that the first column is delimited with a comma, and there could never be another comma embedded within the first column:

perl -pi.bak -e '$_ = ( split /,/, $_, 2 )[1];' myfile.txt
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That works by splitting each line into two parts; the part that comes before the comma, and the part that comes after. The comma is gobbled up. Then take only the second part, and return it back to $_ for output.

You could do it with s/// too:

perl -pi.bak -e 's/^[^,]*,//' myfile.txt
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Here we match everything from start of line, up to and including the first comma, and substitute that match with '' (nothing).