Viral nucleic acid amplification tests use real time PCR to detect viral genomic material. If the genetic material is present, a reaction will occur that generates fluorescence. If sample produces a reaction that reaches a specified fluorescence "threshold" by a predetermined cycle, it will be deemed positive.
The cycle at which a reaction reaches the threshold, is the cycle threshold (CT) value.
If we plot the fluorescent signal generated during the reaction against the number of cycles, it generally follows a sigmoid curve.
Consider this hypothetical plot:
Source: Ian Campbell
As we can see, the black sample fluorescence line crosses the orange threshold line during the 20th cycle. It doesn't happen at the exact beginning of the cycle, but about two thirds of the way through it.
In this case the CT value (dashed blue line) is 20.63.
The reality is that the precision of this value is meaningless, as variability in sample preparation and stochasticity lead to much more difference than a 100th of a cycle.
For more precision, dilution experiments can be performed, but these aren't really necessary / feasible in a clinical testing scenario. See this guide from a real-time PCR thermocycler vendor for more.