Uncertainty, in the analytical or numeric sense, is a topic many people approach with trepidation. However, it is much more approachable and intuitive than it may seem.
Consider the following examples.
First, the local meteorologist has forecast a high temperature tomorrow of 45 °F (7 °C). Suppose I take my thermometer out tomorrow afternoon, let it sit in the shade for a while, and it reads 43 °F (6 °C). Was the forecast wrong?
What if it were 37 °F (3 °C)?
Perhaps a different example may be more familiar. You are on your way to meet a friend for lunch, and you tell them that you’ll be there in fifteen minutes. Seventeen minutes later, you arrive. Were you on time? Were you late?
Finally, here is yet another example, and one I struggle with: you are in a science museum, and the sign next to the T. rex says that it went extinct around 65 Ma. However, there was a paper published two years ago which determined that the Chixulub impact occurred at or slightly before 66.043 Ma (+/-22 ka, 2-sigma). Is the sign on the exhibit wrong?
I hope that from these examples, you can see that uncertainty is something you encounter more often than you necessarily think about. You may also find you have some intuitive sense for what it means and where it might be important.
Here are my interpretations of the above scenarios.
The meteorologist’s forecast is correct. Although it is not usually mentioned, meteorologists in temperate climes expect their one-day forecasts to be accurate to about 2 °F. They have a fairly large area to cover, which may have some temperature differences within it, and there is some uncertainty in the reading given by the thermometer.
When meeting a friend for lunch, being off by two minutes in fifteen is probably fine. Most people understand that such an arrangement may be accurate only to within five minutes. For some people, even five minutes may be well within the understood uncertainty.
As for the museum, I would think it is a great opportunity to teach about uncertainty! On one hand, the casual use of 65 Ma (implying +/-2.5 Ma) is correct. On the other hand, that figure is quite imprecise compared to how well we know when the event happened. Even to the nearest million years, 66 Ma would be more appropriate. This brings up another point: our understanding of geochronology is based on the latest research. Advances in the field, analysis of different materials, or even different interpretations of previously existing data can lead to changes. Despite the great amount of effort put into compiling the best science and geochronology for the latest Geologic Time Scale (mostly not open access, sadly), parts became obsolete even as it went to press. Mostly, these changes are small, and primarily concern scientists who are studying events near these boundaries. If the Cretaceous-Paleogene boundary were to be moved from 66 Ma to 90 Ma, that radical change would need to be backed up with a lot of data, and would necessitate a new sign for T. rex or an acknowledgement that dinosaurs lasted well into the Paleogene (there is no widely accepted evidence that they did).
Hopefully these examples have illustrated that you already have an intuitive understanding of what analytical or numeric uncertainties are and why they are important. In science, where measurements are being made, and calculations based on those measurements are being computed, understanding the uncertainties becomes increasingly important. There are many resources available which outline the process for determining and reporting uncertainties, ranging from a ten-page worksheet to a [very handy and accessible] small book to a comprehensive tome (open access!).
 Renne, P. R., Deino, A. L., Hilgen, F. J., Kuiper, K. F., Mark, D. F., Mitchell, W. S., III, Morgan, L. E., Mundil, R., Smit, J. (2013) Time Scales of Critical Events Around the Cretaceous-Paleogene Boundary. Science 339: 684-687, doi: 10.1126/science.1230492.