What Tithi and Vrat mean
Tithi is a lunar day, one of 30 divisions of the Moon's cycle relative to the Sun, and it's the basis for nearly every Telugu festival and fasting date. A Vrat is a vow, usually a fast, kept on a specific Tithi as an act of devotion, Ekadashi being the most widely observed. Because Tithi is lunar and the Gregorian calendar is solar, the two drift apart through the year, which is why a festival tied to a fixed Tithi lands on a different calendar date each year.
The 15 Tithis, twice a month
Each lunar month has two fortnights, Shukla Paksha (waxing, from Amavasya to Pournami) and Krishna Paksha (waning, from Pournami back to Amavasya), and both share the same 15 Tithi names: Padyami, Vidiya, Tadiya, Chaviti, Panchami, Shashti, Saptami, Ashtami, Navami, Dashami, Ekadasi, Dwadasi, Trayodasi, Chaturdasi, and the fortnight-ending Pournami or Amavasya. The Paksha is what tells two same-named Tithis apart.
Ekadashi and the other recurring Vrats
Ekadashi, the 11th Tithi of each fortnight, falls twice a month, 24 times most years and occasionally 26 when an extra lunar month occurs. Sankashti Chaturthi (4th Tithi, Krishna Paksha) and Pradosham (13th Tithi, both fortnights) are the other two Vrats observed monthly rather than annually, both dedicated to specific deities and kept on their Tithi rather than a fixed calendar date.
Checking today's Tithi, or any date's
The table above covers the next two months of recurring Vrats; for the Tithi on any specific day, including Rahu Kalam and Nakshatra, use the Panchangam page. It shows today's Tithi and Paksha by default and lets you check any other date with the same calculation engine that produced the dates above.