Have you ever been writing along and found yourself writing, "The town was ten miles away," or "The city was thirty kilometers away," or "The gap was about ten feet wide", etc. and wondering if it was the right thing to do? You can't write without ever giving anyone a sense of the scale of things, can you? But if you're writing in a secondary world, or on an alien world where measurements are not the same as the ones we've been using, or in a far future where it seems a bit iffy for measurements to have remained the same, what do you do? And what happens if you're on a planet where days are of different lengths, or working with an interstellar empire where local time is going to vary ridiculously? What then?
I've spent an inordinate amount of time thinking about this because I work in secondary worlds a lot. And basically, there are a number of solutions you can use - which one you pick depends on the context of your world and what kind of "feel" you're looking for.
Option #1A: Use an existing measurement system, directly
Yes, that means using miles or kilometers or feet or centimeters (but unless we're quite close to our own world, probably not both). This can work well for future science fiction contexts where you can plausibly argue that one of our existing systems has been retained. Often in science fiction, measurement and specificity can be important, and you don't just need a measurement system, you need a really precise one that people can easily grasp. Unless you really need to make a major story point about a different length of day or year, etc. you might as well be using days and years and seconds. There's no comparison in terms of ease of use for your reader.
Option #1B: Use an existing measurement system, plausibly
You see this a lot in fantasy, where a world that resembles medieval Europe will use medieval English measurements. Since here in the US we're pretty used to feet and miles, and we've at least heard people talk about leagues, it works well enough for us not to notice it. Not noticing it is, of course, the goal here. We don't want readers struggling every time they have to figure out how big something is.
Option #1C: Use an existing measurement system, in translation
This one is a bit riskier, but let's just assume you've got yourself a really fabulous secondary world or alien world that you're portraying from the insider's perspective - you really can't claim that these people are using the same measurements we would, but you use our measurements anyway, trusting readers to understand that this is just authorly shorthand for what's really going on. It's not actually that hard to do with days and minutes and seconds, or with a person's height (and this is actually what I do with in Varin), but it can require more faith when it comes to measurements of length or distance, where we're more familiar with multiple different options. Watch out for this one and check with your critique partners for plausibility.
Option #2: Use non-standard measurement/compare to objects
This is the one that I use most when I'm working with my Varin world, because it requires no leap of faith on the part of the reader, and because it works wonderfully in a context where the precise measurement of things is not critical to the success of the story. It's not necessarily a problem even when you're dealing with relatively scientific things (for example, medicine can be measured in "doses"). Distance can be measured in "paces." You can measure height relative to a character or to another object of relatively predictable size, like a chair. You can measure distance relative to objects whose parameters have already been introduced. You can also measure distance in the amount of time required to travel from one place to another via a typical mode of transport.
Option #3A: Create a new measurement system that is actually just like an existing one
This is sort of the translation approach in reverse. Give your measurements a new name that fits better with the world they're in, but make them basically function like our existing measurement systems. Again, this is authorial fudging and requires some faith on the part of the reader. However, it can work well.
Option #3B: Create a new measurement system
This one I've found compelling in many ways, but ended up avoiding like the plague. I love the idea that in a different world, or on a different planet, people would measure the things around them differently. However, it takes a lot of work for people to learn a new measurement system. Thus, I really don't recommend this one unless you have a story where the contrast between the local measurement system and the measurement system we're accustomed to is actually a major plot point. There has to be a really good reason to make a reader do this much work, and "well, so they can tell my world isn't our world" isn't a good enough one, at least for me.
It's worth taking the time as you design a world to figure out which of these approaches you're going to take, so that you can make the choice consciously and maintain consistency.