Another way to explain this:
Your cities generate

(Commerce) and depending on the specifics of your cities some will generate more

than others. The main source of

is the tiles inside the city radius (within two tiles from the city tile, roughly) that are worked (not by a Worker unit, but rather by the citizens in your city) and trade routes (which are set up automatically, depending on how much the city already generates, so its self-reinforcing).
The research rate (upper left corner of the interface) determines what portion of the

in your cities will become

(Science). This is the base

of your cities and its multiplied with whatever research related buildings you have in a city. So one city could have 60% of 20

multiplied with +25% (15

) and another could have 60% of 10

without any multipliers (6

).
Your total

is the sum of the

of your cities, and this is what is shown in connection with the research percentage (above). Every Tech has a cost that is counted in

and you accumulate your total number of

toward this goal every turn. Once you have accumulated as many

as the Tech cost you will have researched the Tech in question - and the surplus is added to your next research project.
Was this simple enough?