I'm new to the Civilization series and currently playing my first ever game. I've 3 cities and building a unit in each city seems to require different number of turns - why is this different ? What reduces the number of turns required to build a unit ?
If you click on the city (to enter the city's menu) in the lower left hand corner you will see how many hammers per turn that city is currently creating. Units/Buildings/Wonders have a set hammer cost, the number of turns it will take that city to build that unit is the cost divided by hammers produced per turn (with whatever modifiers apply from bonuses)
In Civ V each city generates its own food, resources, and production from the squares it is considered to be "working". This subtotal is then modified by buildings, wonders, civilization traits, etc. for a final total for each of Food, Production, Gold, Culture, and Science.
Your cities take varying amounts of turns to build things because their "Production" generation is different. Mines and hills generate the most production, but improved bonus resources sometimes increase production as well.
If you want to decrease the time it takes to build the next unit, either increase the production of the city with buildings (by, say, purchasing the Windmill), building mines in tiles around the city, or by changing citizens into engineers.