They are two details that appear on every spec sheet and separate a basic movement from one that is pleasant to use. Neither changes the quality of the watch, but you will notice them every time you set it.
Hacking seconds
When you pull the crown out to the setting position, the seconds hand stops. That lets you wait for another clock to reach the minute and push the crown in at exactly the right moment: the watch is set to the second. Without it, the seconds hand keeps turning while you move the hands and you can only set it to the minute.
Hand winding
It lets you wind the watch by turning the crown. It is useful for starting an automatic that has stopped without shaking it, or for giving it a few extra hours before a day with little movement. Twenty or thirty turns are usually enough to get it going.
The watches without them
Every watch in the catalogue has hacking seconds.
Every watch in the catalogue can be wound by hand.
The rest of the catalogue, 20 of 20 watches, has hacking seconds. It is the norm in modern movements: Seiko brought it to its entry range with the 4R36, and Orient with the F6 family.
Citizen is a curious case: in its 82 series the 8203 does not hack and the 8204 does, and watches using them can look identical from the outside. That is why it pays to check the movement, not just the model. More on the Citizen 82 series page.