Different styles for climbing, each can impact your score.
First of all: points are just here to help you quantify and track your personal progress. There are no rewards other than feeling good when you beat your own best – so don't try to game the system, you're only hurting yourself!
You earn points by completing climbs. A clean 5.2 is worth 1 point, and each grade harder is worth an additional point, such that a clean 5.10b is worth 10 points and a 12.d is worth a cool 20. Climbing outdoors is often harder than indoors, so there is a 1.5x multiplier on climbs outdoors. You'll also earn a small bonus for On Sight climbing and for lead climbing, and you get half as many points if you hangdog a climb. Those are the basics: but don't worry too much about it!
Strava is a very popular app for people to track their various fitness activities, such as biking and running. Strava does not have a good way to track climbing – so we're doing our best with Chalkd.
Anyone can send you a link to their account (in the form of chalkd.app/climber/<username>) where you can follow them. You can also browse the 'firehose' of all public climbs.
If an account is private, you will not be able to see that user's climbs until they have followed you back.
The 5.Xy ratings are the Yosemite Decimal System for rating the difficulty of a climb. Rock climbs start at YDS Class 5 and are rated from 5.0 to 5.15 as they get more difficult, with letters subdividing all ratings from 5.10 up. You will see these ratings at the base of the climbs in most American climbing gyms (Chalkd is an American app).
Bouldering problems use the Heuco or V-scale system, starting with 'V' and ending in a number. The number starts at 0 for the easiest problem and progresses higher as the problems become more difficult.
For more information, REI has an excellent article discussing these rating systems.