The damage cap is an upper limit on how much damage can be dealt in various circumstances. It is not a hard limit - damage values seem to fluctuate around the perceived cap rather than hitting a specific value ceiling, but they cannot significantly surpass it. In general, normal attack damage is capped to 440,000 (440k) damage and Charge Attack damage is capped to 1,650,000 (1.65M) damage. Each character skill also has a damage cap, but the cap varies based on the individual skill.
The 1.65M value is a final damage cap - if a charge attack involves multiple hits during the animation, the final total will not significantly surpass 1.65M. However, normal multiattacks are each separate, so each hit in a triple attack can deal 440k damage. Bonus "echo" damage also is counted separately from normal attacks (see: Warlock's Chaser or Narmaya's Butterfly Effect), so it does not contribute towards the cap.
There are various ways to temporarily increase the damage cap, such as the Kaguya summon or Ferry's Grausam. Most notably, the Hawkeye skill Crack Shot II and similar Break Assassin or OD Assassin skills raise the normal attack damage cap to 1.16M. This means end-game team building is increasingly focused on increasing multiattack rate in order to circumvent damage caps.
Some weapon skills and support skills (most notably Seraphic Weapons) can also raise the damage cap if conditions are met. Conversely, enemies with elemental resistances such as Xeno Showdown bosses take a lower damage cap (up to 50% less) for any element other than their weakness.