A postdoc (also called 'postdoctoral fellows', 'research fellows', 'associate researchers' etc.) is someone who has just finished their PhD and is employed on a temporary research-only contract, usually as a stepping stone to a longer-term position within academia.
Postdoctoral fellowships are a relatively new phenomenon, but are quickly becoming a pre-requisite to building a successful academic career. In case you are thinking of doing a postdoc, here are a few advantages and disadvantages that might help you make a more informed decision.
Advantages of doing a postdoc
If you are absolutely sure you want to stay in academia long-term, doing a postdoc before applying for other types of academic jobs offers a number of advantages:
you have more flexibility than during your PhD, with none of the teaching and admin responsibilities that academics at the beginning of their research career usually have; you can travel freely to conferences and administer your own funds, working hours are almost as flexible as during your PhD
you can devote 100% of your time to research and therefore are able to submit more journal articles based on your PhD, more grant applications, and possibly collect data to be used in future publications
you also have more time to gain new technical and research skills, extend the research undertaken during your PhD or gain expertise in a completely new area, and make a name for yourself in academic circles before looking for long-term academic positions after the postdoc
Due to all these advantages, doing the postdoc can put you ahead of those of your fellow postgrads who start directly with a lectureship, which makes it easier for you to get promoted in years to come.
Disadvantages of doing a postdoc
Despite the serious advantages, you might also want to consider the other side of the coin: doing a postdoc and then not finding a suitable job in academia afterwards. Here's some more food for thought:
most postdocs hoping for an academic post after finishing never achieve this; in the US only 30%, and in the UK only 20 % of postdocs manage to secure a longer-term academic post after the postdoc, and most have to take a succession of post-doctoral positions before achieving a more stable academic position or leaving academia
most postdocs that have to leave academia get little or no career guidance or training, and may be less attractive to potential employees than PhD graduates as they are far too specialised by that stage
you may also encounter poor conditions of employment while undertaking the postdoc; in particular, some postdocs complain of being overlooked as a staff member by their department, very low salaries, not receiving specific job duties or job description, and constantly being stressed about their financial situation due to the short-term nature of postdoc contracts
All things considered, it does seem like the decision about whether or not to do a postdoc might largely depend on how committed you are to staying in academia long-term. If you can be sure you definitely want to stay, then you might be better equipped to deal with the lack of security during your time as a postdoc. However, consider asking for as much advice as possible from your supervisor and other academic staff before deciding to say yay or nay to the opportunity to do a postdoc.