DPS, which many can recognize if you have played an MMO, FPS, or RPG, is the abbreviation for damage per second and it is a meter for how fast you take down enemy and boss health meters.
At low stage levels (1-50), almost 100% of your total DPS is from your player's skill levels.
When you hit 400 - 500 player levels, it is highly recommended not to level any more until you want to prestige* as leveling your heroes now gives you much more DPS for gold spent. It is up to you to judge what to level as it depends on how many artifacts you own, their respective levels, hired hero buffs, and how many weapon upgrades for those hired heroes you have obtained.
As a good note, the normal total DPS can be approximated by taking your tap damage and multiplying it by 10 and adding it to your hired heroes' DPS.