Apols is a very simple and arguably stupid word: it is simply an abbreviation of word "apologies." So, instead of saying "My apologies to the bride, but I don't want to get married," you can save yourself two syllables and say "my apols to the bride, but I don't want to get married."
Why is this a thing?
In these modern times, people feel the need to abbreviate anything that can be abbreviated and apologies is one such thing. It makes sense on some level since there really is no noun for multiples apologies besides well, apologies. You can't say "my sorries to everyone who has to re-read this," you have to say my apologies. Why not cut out the middle man, 'ogie', and stick to the apols.
Here's a picture of someone using the word:
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