Most keyboards still have staggered keys. This heralds back to the days of typewriters when physical hammers had to swing forward and smash ink into paper. Each row was staggered to allow these mechanical hammers to avoid smashing into the rows above it. This worked well for the typewriter, but not so much for the typist. Our fingers are designed to move straight up and down, not side to side. To further complicate things, keyboards have now become much larger than the original typewriters. This means that there are more keys staggered way up and away from where your fingers naturally rest on the keyboard. This means that it's difficult for many people to hit far-away keys without looking at their hands because nothing is in a consistent spot. Obviously, this traditional key stagger is no longer mechanically necessary, so the only thing keeping staggered keys popular is tradition.
Ortholinear is just a fancy way of saying "laid out in a grid." Ortholinear (or Ortho, for short) keyboards seek to address the issues of traditonal staggered keys by aligning all keys in a grid. This means that your fingers get to move straight up and down while typing, which makes a lot more sense with how your hands are designed. This grid layout also has a nice side effect of bringing all keys into easy to find locations. You now only ever have to move your fingers straight up or down to find what you are looking for. For example, instead of your 1 key being somewhere off in the far top left corner of your keyboard, you just need to move your pinky straight up two rows. No peeking required! Because of this, Ortho keyboards make touch typing (typing without looking at your hands) much, much easier.
Columnar keyboards have all the same benefits of Ortho keyboards, but with one additional nicety. Your fingers are all different lengths, so why should your pinky have to reach just as far as your middle finger when hitting keys on the top row? Columnar keyboards look out for the little guys by staggering each column of keys according to the lengths of each of your fingers.