What is the significance of the numbers?
They represent ratios that determine a dovetails angle. So in the case of 1:6 - for every unit you move up you also move 6 units over. These ratios are not usually mixed or changed on a single project. A simple trick to getting perfect angles, and to illustrate my point, uses a bevel guage and square. The always amazing Roy Underhill demonstrates this in this video "The Dovetail Variations"
Hard to tell from the picture but the bevels handle is resting so the guide
itself is crossing 1 inch and 6 inches.
Using these tools the traditional woodworker could easily transfer any ratio to wood.
Of course there are many manufactured guides available as well that maintain these angles for you.
Below is a table that corresponds common ratios to angles. This way you can use whichever you are more comfortable with.
[D]oes it matter which ones I use?
There are a couple of schools of thought in this regard. In general many favour the 1:6 ratio but you will run into many who suggest using different ratios for hardwood and softwood. 1:8 for hardwood and 1:6 for softwood. However the exact ratio / angle is not important. What is important is the integrity of the overall joint. Glen D. Huey on a PopularWoodworking article words this sentiment well
What’s important is that you don’t get the slope so steep that your tails break off and your joint caves. Or that you don’t get the slope too straight that your tails slip from the pins, or that your joint has to rely only on glue for its strength. Between those two extremes anything goes.
If your tail breaks off while assembling the joint one of the considerations might be your angle is too steep...