What was ticking just after the Big Bang? When reading about the Big Bang, I see phrases like 3 trillionths of a second after...  So, what was ticking to give a time scale like this? We define time now in terms of atomic oscillations, but these effects occurred before there were any atoms, or anything else, oscillating to give a reference to measure time against. 
A similar question has already been posted, but the esoteric answers there do not give me a way of visualising what information these time intervals are really intended to convey.
 A: As dmckee points out in his comment on your question - There's a difference between defining a unit of time, and defining time. 
There are several ways to define our units of time. We could define it in terms of atomic transitions or in terms of distant stars or from pulsars or from the sun. 
These are all different ways of measuring time for different purposes. But we can always imagine breaking up time into arbitrarily small chunks. By this I mean we don't as yet know whether time and space themselves are fundamentally quantized or if there is another physical limitation which will make measuring arbitrarily small units of time and space impossible. So in theory, we can always hypothesize what will happen at infinitesimally incremental times.
A: dmckee made an astute point that time is not the same as units of time. Today, we have a very well-defined notion of time since the time scale of the vibration of atoms is much smaller than the age of the universe. If I think of time as a coordinate in $ds^2=dt^2-dx^2-dy^2-dz^2$ (Minkowski spacetime, for example), the (timelike) interval between two events $dt$ is still a well defined concept for very small intervals. By that, I mean suppose the time interval for an atomic vibration is $\Delta t=1$ (arbitrary units), I may still talk about time on scales of $\Delta t=0.001$ since $dt$ can be made to be arbitrarily small*, I just won't be able to build a clock that uses atomic vibrations to measure time since the clock itself would not have the necessary precision to differentiate between time $t=2.000$ and $t=2.001$.
This leads to the question what can we use in place of a clock that measures in atomic vibrations. In cosmology we may choose proxies for the time coordinate $t$ such as temperature, size of the universe, or average density. (This is of course assuming we possess a decent understanding of the physics at these epochs and how these quantities relate to each other.) For example, we believe that the universe was radiation dominated from the era of reheating until matter-radiation equality, and the physics are well understood. 
In a radiation dominated universe, I can calculate the scale factor $a(t)\propto t^{1/2}$, temperature $T(a)\propto 1/a$, and density $\rho(a)\propto a^{-4}$. Using these relations, I may use time, size, temperature, density interchangeably. These relations allow us to make statements about time scales smaller than clocks are able to measure.
$*$ By arbitrarily small, I mean classically arbitrarily small. Quantum effects will be a whole other interesting story.
