Runout is the lack of alignment between the bullet and case. You can measure it by placing the case in a v-block and putting a dial indicator on the bullet, then spinning the case in the block. If it’s really bad, you can roll the loaded cartridge across a table and see the tip wobble. It doesn’t always cause problems. I’ve seen great groups shot with bullets seated visibly crooked. GENERALLY runout is less important when a bullet with a long tangent ogive is seated long in a case with a thin neck and low neck tension. With very little of bullet in the case neck, and plenty of contact with the lands, the lands can align the bullet to themselves to some degree. Runout becomes a bigger issue when the above factors go the opposite direction. More bullet in the case neck, increased neck tension and secant ogives can make it difficult to realign the bullet when it’s chambered. Jumping a bullet instead of jamming causes that realignment to take place very rapidly while the bullet is moving. Secant ogives interface with the lands much more abruptly. Thick necks require more force to realign a bullet even with low neck tension.
High bullet runout can be caused by dies that don’t properly align a bullet with the case, or by brass with necks that are thinner on one side than on the other.
Actual magnitude of neck tension is not as important as consistency of neck tension. Inconsistent neck tension can come from inconsistent neck thickness from case to case, or inconsistent hardness. Mixing brands, or cases that have been fired ten times with cases that have been fired once will give you differing neck hardness. Harder brass springs back more after sizing than soft brass, and thus gives you inconsistent neck tension. High neck tension, and thick necks tend to exacerbate issues with inconsistent neck tension, so even if the amount of neck tension isn’t the real culprit, turning necks and changing bushings or expander buttons can eradicate issue with inconsistent neck tension.(turning necks can improve runout as well, but you really shouldn’t have to turn necks to get well under 1-MOA) Check your sized case neck diameter, and if it’s much more than .001” smaller than your bullet, you MIGHT benefit from reducing your neck tension a little bit. Check your expander button and see if there’s any chance you got one that was smaller than spec.
Also, even with little to no bullet runout a cartridge that sits loosely in a chamber leaves the bullet misaligned to the bore. Seating out long enough to touch the lands, especially with a tangent ogive bullet, can properly align the cartridge in the chamber to some degree. Jamming a bullet into the lands is not always recommended for hunting loads because it’s possible to open the bolt and come out with an empty case, an action full of powder, and a barrel with a bullet lodged in it. Partial or neck sizing can help align the cartridge to the chamber. Both partial sizing and neck sizing can result in a stiff bolt close and lift, so again, they are often not preferred for hunting. Those techniques have fallen out of favor among competitive shooters as well, but competitive shooters are using custom chamber reamers and custom dies that allow them to full length size and still have a near perfect fit in their chambers. In a factory chambered rifle, it’s possible to have situation in which sizing the shoulder back enough to chamber easily results in sizing the case diameter down too much and thus leaving it a little sloppy.
Make sure your seater die isn’t set up where you’re slightly crimping the case mouth. Although that doesn’t usually result in great accuracy even when done properly, if you happen to be very very close to the crimp portion of a seater, and you have inconsistent case lengths, you can have some bullets that are barely crimped, and others that are not crimped at all. Also check your case lengths. If they need to be trimmed, it’s possible to have some case neck in the throat, which will result in a very similar crimping. If it gets excess it can lead to serious problems with overpressure.
Some guns, and some barrels, just won’t shoot.