If you are beginning with ukulele and have no string instrument background, you may be confused by this oft used phrase - what is it though, and why should you be worried if it is bad?
Intonation refers to the ability for a ukulele to be in tune not just when the strings are plucked "open" but also when fretted anywhere else on the neck. Bad intonation will basically mean that your uke wont play in tune even if your strings are tuned perfectly when open.
Its down to mathematics. The position of the frets on the neck are placed accurately in relation to the scale length of the instrument (distance between nut and saddle). When set correctly (and assuming the instrument is set up well) holding a string at any fret and plucking will give you precisely the note that is supposed to be played at that fret (see my fret roadmaps on chord page to check them HERE )
If you find that your uke, despite being tuned correctly is sounding bad at certain frets, it could be a number of factors, from easy to difficult. In line with my earlier post regarding buzzes, have a run through this checklist in order to see if you can isolate the problem
1. Bad strings? A badly made string can cause tuning problems along its length - try swapping the string to see if that cures it
2. Action at the saddle - this refers to the height of the saddle. If a saddle is too low, it can cause buzzing but equally, if too high, can cause problems with intonation. Again, this comes down to mathematics (switch your brain on and think of pythagoras!). For the maths to work, and the frets to accurately give you the right notes, it assumes that the strings run as close as possible as to be parallel with the line of the fingerboard. If you imagine a seriously high saddle, the strings will run at an increasing height away from the fingerboard approaching the bridge - like the hypotenuse of a long thin triangle - if this is the case, your open tuned string will sound fine, but you are stretching and pushing the string down when fretting and this will give you an off note. The answer is simple - sand the saddle base down and re-install, taking care not to sand too much or you will get buzzing -the answer is to do it a little, replace it, repeat.
3. Action at the nut - this is tricker to deal with, and may be something you give to a luthier. Again if the nut slots are too high, you get same effect in reverse. To lower nut slots be very very careful and I would recommend using nut files especially for the purpose.
4. High frets? - in some cases high frets can cause problems as the string will have to dip down as you press it and stretch - characteristics of this are a note that sounds fine held softly but sharpens when you squeeze - dramatic cure is to have the frets dressed down, but much easier fix is to play the uke a little lighter with your fretting hand!
5. Something more serious - sadly, if the above dont fix the issue, you are looking at a badly made uke or a neck out of alignment. Either get a refund, or it its a valuable oldie - look for a fix.
At the end of the day, if you are buying new, the best way to avoid this is to physically play before you buy - take a digital tuner with you and test the thing. If thats not possible though, I hope the tips above show that a lot of issues are easily fixed.
Buying cheaper ukes in particular tends to raise the chance of intonation issues, but usually its just a string or saddle issue that will fix it. Beware - even top end instruments with bad set up can slip through the net!