There is considerable debate as to just how important domain age is when it comes to search engine optimization. There does seem to be a general belief that it is easier to rank an older domain but the reason behind this is in debate. There is also a lot of debate as to just how much an older domain will help in getting your site to rank. The bottom line is that an aged domain will give you a head start but ultimately you can get any domain to rank well.
There are a few different theories as to why domain age is important. The main one is that an older domain should have more and better content than a newer domain. The search engines goal is to make sure the top results give the best content to the searcher so the theory goes that they believe that the content on an older domain will be better than the content on a newer domain. The reasoning seems to be that since somebody has kept paying to keep the domain active they would most likely have been adding content to it so the site must have better content than a new site. Whether this is actually true or not is debatable but it does seem to be a factor in ranking sites.
The other main theory as to why domain age matters in search engine rankings is that spammers are unlikely to pay for an older domain. This actually makes sense since spammers will just purchase hundreds of domains and put up a whole bunch of low quality sites hoping to make a few dollars from each one. In order to have an aged domain you are either going to have to let it age before you use it or you are going to have to buy an aged domain. Either way this is going to be a major hassle for the spammers so they usually don't bother. Especially since there is a good chance that their spam sites are going to be de-indexed eventually anyway.
This brings up the question of whether or not you should buy an aged domain for your website. There are no easy answers to this question because you likely will find it easier to get an aged domain to rank; on the other hand you are going to have to pay more for the aged domain. The decision is largely going to come down to whether you want to invest more time or money. Obviously if you go with a new domain it will eventually get ranked, if for no other reason than that it will age while you own it. On the other hand having an aged domain will give you a head start. You are going to have to factor in how much an aged domain costs and how competitive the niche that you are targeting is in order to decide if buying an older domain is a good idea.