I am Swedish and am just trying the Swedish course to see how accurate it is (so that I know if it is worth doing other languages). This answer is wrong. I would say that the translation should be 'one moment please', however this phrase is not something I would use in Swedish anyway as you would just say 'Ett ögonblick'
Most people here are assuming that we're asking someone to wait a second and therefore it should be "hang on a moment" or "one second please" or whatever, but there's nothing inherent in the phrase to suggest that this is what it means. While I agree with all the other native English speakers that we'd not say "a little moment" or a "small moment", we COULD absolutely say "a brief moment", or "a short moment" like "Oh, sorry, for a brief moment I thought you were someone else." or, as rz.lx said "We had a little moment" which could mean a lot of things. It doesn't have to be romantic, but I think the reason that "little" in this context sounds OK is that "a moment" is not (in this setting) a measurement of time and therefore by definition, small, it's just a connection that you can't quite put your finger on, or something like that. It can therefore be little, or not so little. In fact, now I think about it, racing car commentators use "moment" to mean, a second where the driver looked as though they were going to lose control. They therefore say "Whoa that was a big moment there for Lowndes, he almost collected the wall over Skyline there, I'm not sure how he held on to that!" In this setting, the moment is always short, but it can very very short, or a bit bigger and pronounced.
In summary: if this is about "waiting a moment", then it can't be "a little moment", but it could conceivably be so in other settings.
Unfortunately the etymology is not that interesting. It's just a compound word of "ögon" ("eyes") and "blick" ("glance"). Compare the English phrase "in the blink of an eye". While it's true "glance" and "blink" aren't the same thing, they give the same impression of something to do with eyes happening very fast.
"Ögonblick" can technically translate to "blink of an eye", but I think it needs "på" (depending on context) to make up that phrase. "På ett ögonblick" = "In the blink of an eye". Don't forget the word "litet" here. You may be able to say "in the short blink of an eye" if you want to be poetic or something, but I wouldn't call it a set phrase.
There's a great expression in Swedish – Vad rätt du tänkt, fast det var/blev fel 'How right you thought, though it turned out wrong'. This is an old parody – the very high minded poet Viktor Rydberg wrote some very solemn poetry that said among other things
Vad rätt du tänkt, vad du i kärlek vill,
vad skönt du drömt, kan ej av tiden härjas, http://runeberg.org/rydbdikt/kantat.html
… in 1877. But then later on, the comic poet Nils Hasselskog (who died in 1936) paraphrased it as Vad rätt du tänkt fast det var fel which gives a whole different effect of course.