The Islamic calendar is a purely lunar calendar. Each month begins with the sighting of the new crescent moon and is either 29 or 30 days long. A lunar year is approximately 354 days, compared to the solar year's 365 — a gap of about 11 days.
This is why Ramadan falls in different seasons over the years — in some decades it comes in summer, others in winter. The same is true for Hajj, Eid, and every other Islamic date. There is no intercalation (adding a leap month) as there is in the Jewish calendar, so the Hijri calendar rotates freely relative to the Gregorian one.
The calendar year counts from the Hijra — the Prophet Muhammad's ﷺ migration from Mecca to Medina in 622 CE. The current Hijri year is 1446 AH (Anno Hegirae).
Allah mentions in the Qur'an (9:36) that He designated four months as sacred (Haram): Muharram, Rajab, Dhul Qa'dah, and Dhul Hijjah. Three are consecutive and one stands alone.
During these months, certain acts of aggression were forbidden in pre-Islamic Arabia — a social convention Islam confirmed and gave divine sanction to. Scholars differ on whether there are additional acts of worship or restrictions specific to these months beyond what applies year-round. What is agreed is that sins in these months carry greater weight, and therefore so do acts of worship.