Alternate fingerings can be used to compensate for intonation problems that are unique to a particular instrument. They are also useful when you have a rapid slurred passage in which two or more consecutive notes have the same fingering. (Just use a different fingering for one of the notes.)
The note that you want to play is a certain number of semitones down from any “open” note above it. For example, on a BBb tuba we might play the Db in the middle of the bass clef staff with the second valve, because it is one semitone below open D. But there is an open F above that D, which may have better intonation. By counting semitones down the chromatic scale from F to Db we see that we need a fingering that will bring the horn down 4 semitones. Looking at a fingering chart, we find that the Db can be fingered 23. You probably knew that already, since the same fingering works an octave lower.
But there is also an open Ab (top line of the bass clef staff, called the "seventh partial") that is not normally used by tuba players because it is very flat. (Trombonists use it all the time, because they have a slide that moves easily.) That Db mentioned in the previous paragraph is 7 semitones down from that high open Ab. There are three possible fingerings for the 7th semitone: 14, 124, and 34. The latter two will be flat, and we don’t want that because the open Ab that we are starting from is already flat. But the 14 fingering is roughly 46 cents sharp, and that will tend to compensate for the flatness of the open note. If your electronic tuner tells you that the high open Ab is roughly 40 cents flat on your instrument then this 1-4 fingering may work pretty well for you.
In general, a sharp fingering used on a flat open tone can result in a useful alternate fingering. For example, middle Ab (lowest space on the staff) fingered 123 or 24 works pretty well on some BBb tubas.
Here is another example: A student with a new and very expensive euphonium found that her Eb above the bass clef staff is very sharp. To correct it she had to pull the first valve slide out almost two inches. Of course that made other notes very flat if she didn't remember to push it back in. We figured out that she could take advantage of that flat open Ab mentioned above by using her fourth valve instead of her first valve for that high Eb. Her instrument wants to make the Eb sharp, but the seventh partial wants to make it flat; the two effects cancel.
If there are one or two notes on your tuba that are consistently too flat or too sharp sometimes you can reduce the severity of the problem by keeping one of your valve slides at a slightly different position and then using some alternate fingerings. With a spreadsheet you can find out how such an adjustment can be expected to affect all of the rest of your notes. For example, I might really like using first valve on a BBb tuba for C in the staff, but it might be too flat because of the flatness of the open D above it. I could use a different fingering (such as 4) or I could shorten the first valve tubing. That makes my Ab’s a little high, but not badly. But it then makes my “G” (12) seriously sharp. So I use 3rd valve for that note, instead. By putting a smaller value into the spreadsheet for the length of the first-valve tubing I can see how that change will affect the pitches of all other fingerings.