A cron expression is five space-separated fields, minute, hour, day-of-month, month, and day-of-week, each of which can be a single value, a range like 9-17, a step like */15, a comma-separated list, or a wildcard meaning "any." The parser here reads any expression back into a plain-English description and computes its next 10 actual run times by simulating minute-by-minute forward from now, while the builder panel lets you construct a valid expression field by field without memorizing the syntax.
The */N syntax means "every Nth value starting from the field's minimum", for minutes that's every 15 minutes starting at :00, giving you :00, :15, :30, and :45. The same pattern works in any field: */2 in the month field would mean every other month starting from January.
Standard cron treats these two fields as an OR, not an AND, whenever both are restricted away from *, meaning the job runs if the date matches either condition, not only when it matches both. An expression like 0 0 1 * 5 runs on the 1st of every month AND every Friday, not just Fridays that happen to fall on the 1st, and this parser follows that same rule when computing run times.
They're computed using your browser's local time zone, since everything runs client-side with no server involved. If the cron job actually runs on a server in a different time zone, its real trigger times will be offset from what's shown here by that time difference.