The distance a creature can jump is determined both by the method attempted and their Strength score.
A running long jump requires a creature to move at least 10 feet by foot immediately before making its jump and the distance covered is a number of feet up to its Strength score. To make a standing long jump, a creature need not move beforehand, but only jumps half the distance it would have doing a running long jump. Each foot covered by a jump costs the same in movement.
The DM can also request a DC 10 Strength (Athletics) check to clear low obstacles, which must be no taller than a quarter of the jump’s distance. A failure indicates that instead of jumping over such an obstacle, a creature crashes into it.
Landing is also a fair challenge. Should a creature land in difficult terrain, perhaps jumping over a table in the kitchen only to land on a freshly mopped floor on the other side, the creature must make an additional DC 10 Dexterity (Acrobatics) to actually land on its feet. Should it fail, it instead falls prone.
A high jump is a bit more complex. To make a running high jump, a creature must move 10 feet on foot immediately before the jump, leaping up into the air a number of feet equal to 3 + its Strength modifier (minimum of 0 feet). To make a standing high jump, a creature need not move beforehand, but only jumps half the distance it would have doing a running high jump. Each foot covered by a jump costs the same in movement.
A creature can extend its arms up to half its height during a jump. Thus a creature can reach above itself equal to the height of a jump plus 1.5 times its height. In addition, the DM may allow a creature to make a Strength (Athletics) check to jump higher than it could otherwise.
In certain cases, such as being under the effect of the Jump spell, when a creature’s jumping distance exceeds its Speed, it can jump the maximum allowed distance (three times the creature's normal jump distance in the case of the Jump spell) in a single leap so long as it takes no other movement on that turn other than to jump, and any requisite movement for the type of jump they are attempting (ie, the 10 feet of movement required prior to jumping for a Running Long or High Jump). In either case, a creature uses up a foot of movement for every foot it covers jumping.