For anyone new to Destiny 2, there's a lot to learn. It's confusing to know what to do, and when. The game also does a fairly weak job of explaining what's available to you, and what your routine should be. Challenges are an integral part of Destiny 2 as they're a key avenue for obtaining powerful loot and rewards. Most Challenges are easy to complete, and either come in the form of a daily or weekly "challenge".

It's also important to note that Bungie adhere to the following:

Daily Challenges reset everyday at 9AM PST / 12PM EST (10AM PDT / 1PM EDT during Daylight Savings Time for regions that observe it).

Challenges for activities that refresh weekly (Nightfall Strikes, Raids, Trials of the Nine) reset every Tuesday at the same time as the daily reset.

Challenges can be identified as available by the gold star symbol next to a specific planet or location. 

Selecting on that location will then show you the NPC's that are offering Challenges for the day/week (a light blue icon with a white star). Accepting Bounties from these NPC's (which you then complete), or undertaking Public Events (such as the Vex Invasion Challenge) will see them completed and rewards obtained automatically. Progress of active Challenges (Vex Invasion) can be tracked by opening your Ghost (TAB) and is on the right-hand side of the screen. Passive Challenges (such as Zavala below) you track the progress of by returning to him on the map. 

While there's no requirement to complete Challenges, if you've reached the point in the game where you've exhausted all the story content (and have completed Shadowkeep), there's absolutely no reason not to pick them up. The rewards are good, you gain additional Tokens which you can then spend, and you also gain Glimmer along the way.