takin' 'er easy

usually when you see a comment like that using the colloquial (not formal English) contraction " 'er ", it is a substitute for the word "her".

In this usage, "her" isn't really referring to anything specific. Again, it is a colloquial expression which, in a very technical explanation, which personifies "Life" (or a situation one has run into in life) as a female and so "time for taking 'er easy" means time to step back and observe, time to relax a little about whatever the issue is...time for taking 'er (her or it--life) easy."