Pitru means ancestors and Paksha means fortnight. Pitru Paksha is the fortnight that belongs to the ancestors. It is the ideal time to worship our ancestors, do Tarpan or Shrādha ritual for them, seek their blessings and pray for their liberation. Pitru Pasha every year starts on the Full Moon (Poornima) of Bhadrapada lunar month and lasts until the following New Moon (Amavasya). This year (2022) it is from Sep 10 through Sep 25. The ancestral plane is closer to the Earth during this fortnight. Think of all your ancestors, your lineage. Offer incense to ancestors. Light a ghee lamp each of these 15 days.
Here are some powerful mantras you can chant for ancestors especially during pitru paksha:
ॐ पितृभ्यः नमः । Om Pitribhyah Namaha
ॐ देवताभ्यः पितृभ्यश्च महायोगिभ्य एव च । नमः स्वाहायै स्वधायै नित्यमेव नमो नमः ॥ Om Devatābhyah Pitribhyah Cha Mahāyogibhya Ev Cha | Namah Swāhāyei Swadhāyei Nityameva Namo Namaha ||