In the BBC, each season of Doctor Who (as well as all other programs) is actually referred to as a "series". And this is the key. Shows tend to be renewed by the BBC on a series-by-series basis, unlike some shows in the US that are given multi-season renewals. Due to a mixture of limited budgets, long production times (often due to union regulations that limit how many hours a production may work during a 24-hour period) and a general belief in quality vs. quantity, most series produced by the BBC have shorter seasons than those of US networks (though this is rapidly changing with more US-produced shows like Game of Thrones producing short-term seasons). Most seasons/series of Doctor Who since its return in 2005 have been 13 episodes in length, though Series 8, broadcast in the fall of 2014, was only 12 episodes due to several episodes most notably "Deep Breath" being longer than the standard 45-minute length. A Christmas special is also commissioned each year, and it generally is not considered part of any season, though it's usually rolled into the following season for the purposes of DVD/Blu-ray season set release. An exception was the 2012 Christmas special, "The Snowmen", which was confirmed by Steven Moffat in Doctor Who Magazine as being considered part of Series 7, thereby bringing that season to 14 episodes.
The BBC is not obligated to air shows year after consecutive year, and as a result "gap years" occasionally occur for various reasons. (For example, the sitcom Red Dwarf had a four-year gap at one point between seasons during its original run). Doctor Who has had three gap years in its history: 1985-1986, 2008-2009, and 2013-2014. In all cases, special productions were commissioned to fill the gap somewhat ("Slipback" (audio story), a radio play; a series of five special episodes dubbed the "Series 4 Specials"; and the anniversary/Christmas specials "The Day of the Doctor" and "The Time of the Doctor", respectively).
Despite the relative brevity of its seasons, the BBC has also allowed/required the modern era of Doctor Who to air "split-seasons" on a couple of occasions, to spread the series throughout the year, or to allow the production team to separate different "eras" of the show. this occurred with Series 6, which was split between spring and fall mini-seasons, and with Series 7, which had a fall 2012 season, a Christmas special, and then a spring 2013 season that was thematically and stylistically different enough from the first half to be considered a separate series by some. No such split is planned for Series 8. Although some criticized the BBC and Moffat for doing this, split seasons have been around for a while and are growing in popularity, with the 2000s revival of Battlestar Galactica, Mad Men and Breaking Bad (among other series) all splitting seasons, sometimes with a year or more interval between parts.