h''v -- abbreviation for Chas v’Shalom, meaning “God forbid”
Ha'adama -- shorthand name of blessing recited before eating vegetables
Ha'aitz -- shorthand name of blessing recited before eating fruits
Ha'gafen -- shorthand name of blessing recited before drinking wine or grape juice
hach'nasat orchim (hach'nasas) -- lit.: welcoming guests; the special mitzvah of hospitality
Haftorah -- selection from the book of prophets read after a public Torah reading
hagbah -- the honor of lifting the Torah for all to see, following the completion of a public Torah reading
Haggadah -- lit.: telling; book that is read at the Passover Seder
HaGomel -- blessing recited upon being spared from a dangerous situation -- e.g. completion of an overseas journey land, recovery from major illness, and being released from captivity
HaKadosh Baruch Hu -- he Holy One, Blessed is He
hakarat hatov -- lit.: recognizing the good; gratitude
halacha -- lit.: path; Jewish law
Hallel -- special prayers of praise recited on festivals and Rosh Chodesh
hamentashen -- triangular cookies eaten on Purim; said to resemble the shape of Haman's ears
Hamotzee -- shorthand name of blessing recited before eating bread
Hashem -- lit.: the Name; common way to refer to God
hashgacha -- ritual supervision; most often used in terms of kashrut
hashkafa -- lit.: outlook; the Torah viewpoint on any particular issue
Hatikvah -- lit.: “the hope”; the Israeli national anthem
hatmana -- the rabbinic prohibition of insulating a food to keep it warm
Havdallah -- series of blessings recited at the end of Shabbat and holidays, marking a distinction between the holy day and the regular weekday
hechsher -- kosher certification
hesech hada'at (hada'as) -- lit.: removing your thoughts; decision to stop eating a meal or snack
heter -- lit.: permission; a rabbinic ruling that permits something
hiddur mitzvah -- performing a mitzvah in the optimal way, and/or enhancing the esthetic aspect of a mitzvah
hitpa'alut -- (colloquially, his'pie'lus) a form of Jewish meditation
Hy''d -- abbreviation for Hashem yimkom damo, meaning “God should avenge his blood”; used as an appellation for someone who was murdered by anti-Semites