Yes, it means 'over-analysing' something - treating a situation as more complicated than it actually is.

The analysis part is what makes it overthinking, not whether or not it makes something take longer or not. The taking longer or hesitation might be a side-effect, but you don't have to hesitate or take longer to do something in order to overthink something. You could overthink something that has nothing to do with any kind of action what-so-ever. I used the expression in an Italki discussion recently in exactly that way. There was nothing that got delayed, nothing that wasn't done, no hesitation. I just said that someone was overthinking a particular point I had made.

This is an entertaining article on the topic, if anyone's interested http://moreintelligentlife.co.uk/content/ideas/ian-leslie/non-cogito-ergo-sum

To overthink something is pretty much as Su.Ki. said. It is to add more issues to thinking about a situation or decision than is necessary. The result of doing this is either to hesitate to make a decision as Camilo wrote or to make the wrong decision altogether. Consider this situation: A: I want to ask her for a date but I'm afraid that she won't want to date me because I'm a graduating senior and it will be hard to have a relationship after I graduate. B: You're over-thinking the situation. It's just a first date. Go ahead and ask her out and worry about the future later. As an extra gift, unwarranted hesitation due to over-analysis is jokingly referred to as "analysis paralysis".

To overthink is precisely what Su.Ki. wrote below. The synonym would not be to hesitate, but rather to over-analyze.