As player characters overcome challenges, they gain experience points. As these points accumulate, PCs advance in level and power.
From the Pathfinder Core Rulebook, p. 407, the paragraph titled "Experience Points":
"Thus, assuming the medium XP progression, a 20th-level character
needs 2,100,000 XP to become 21st level, since he needed 1,050,000 XP
to reach 20th level from 19th."
Consulting Table 3-1: Character Advancement and Level-Dependent Bonuses on page 30, we find that for medium advancement, 19th level is 2,550,000 and 20th level is 3,600,000. The difference between these is 1,050,000. So the first reference implies that the experience levels in the table are cumulative, since the difference is what's required to advance.
From the Players Handbook I v 3.5, p.58, under "Experience and Levels":
Experience points (XP) measure how much your character has learned and how much he or she has grown in personal power. Your character earns XP by defeating monsters and other opponents. The DM assigns XP to the characters at the end of each adventure based on what they have accomplished. Characters accumulate XP from one adventure to another. When a character earns enough XP, he or she attains a new character level.
"When your character's XP total reaches at least the minimum XP needed
for a new character level (see Table 3-2), he or she "goes up a
level". For example, when Tordek obtains 1,000 or more XP, he becomes
a 2nd-level character. As soon as he accumulates a total of 3,000 Xp
or higher (2,000 more than he had when he gained 2nd level), he
reaches 3rd level."
Looking at Table 3-2 on p. 22, we find 2nd level at 1,000 XP and 3rd level at 3,000 XP, and the text quoted above indicates that the values in the table are totals, and that only the difference is required to advance.