Why Latin at all
Latin was the administrative and liturgical language of Western Christendom for a millennium. It persisted in Catholic parish registers into the 20th century and in Anglican, Lutheran, and Reformed registers for centuries. Legal documents drawn up by clerks trained on Latin forms kept the shorthand even when the surrounding prose shifted to English. Most of what you will encounter is not grammar — it is single-word abbreviations acting as column headers or margin notes.
Family and relationship
Ux. (uxor) — wife. Relict (relicta) — widow (literally 'left behind'). Pat. (pater) — father. Mat. (mater) — mother. Fil. (filius or filia) — son or daughter. Frat. / soror — brother / sister. Vid. (vidua) — widow. N.n. (nomen nescio) — 'I don't know the name', used when a parent's name is unknown.
Dates and life events
Nat. (natus, nata) — born. Bapt. (baptizatus) — baptized. Conf. (confirmatus) — confirmed. Obiit — died. Sep. (sepultus) — buried. Aet. (aetatis) — aged (followed by a number). Anno — in the year. A.D. (anno Domini) — in the year of the Lord. The common '5 aet. 48 an.' reads as 'aged 48 years'.
Legal and probate
Et — and. Et al. — and others. Et ux. — and wife. D.b.n. (de bonis non) — of the goods not yet administered. Exr. (executor) / admr. (administrator). Per stirpes — distribution by branch of the family. Per capita — distribution by head. In ventre sa mère — unborn at the father's death.