What does B”H mean at the top of a letter?

“Baruch Hashem” or “Be’ezrat Hashem” (with God’s help). BS”D means “with the help of Heaven” in Aramaic.

Why do Jews write G-d?

Out of respect, to avoid erasing or discarding God’s name. It is a custom; many authorities say the English word has no formal sanctity.

How is Baruch Hashem used in conversation?

As an answer to “How are you?” (“Baruch Hashem, good”), or to thank God when sharing good news.

What does Hashem mean?

“The Name” – a respectful way to refer to God in everyday speech.

Baruch Hashem and B”H – meaning and use בָּרוּךְ הַשֵּׁם

“Baruch Hashem” (בָּרוּךְ הַשֵּׁם) means “blessed be God” – literally “blessed is the Name”. It is the classic answer to “How are you?” and an everyday way to thank God for anything good.

The source

When Jethro heard of the Exodus he said “Baruch Hashem, who saved you from the hand of Egypt” (Exodus 18:10), and Abraham’s servant used the same words when his mission succeeded (Genesis 24:27). Thanking God aloud for good things is a basic Jewish attitude; the Talmud even counts the many blessings a person should say every day (Menachot 43b).

Why “Hashem” and “G-d”?

The four-letter name of God is not pronounced, and other names of God are said only in prayer and blessings (Pesachim 50a). In everyday speech Jews say “Hashem” – “the Name”. The Torah forbids erasing God’s name (Deuteronomy 12:3–4, as explained in Makkot 22a), so many avoid writing it in full on paper that may be thrown away; in English some write “G-d”, in French “D.ieu”. Many authorities hold that the word in a non-Hebrew language has no such sanctity, but the custom is kept as a mark of respect.

B”H and BS”D

Many Jews head letters and documents with “B”H” (בס״ד or ב״ה). ב״ה stands for “Baruch Hashem” or “Be’ezrat Hashem” (with God’s help); בס״ד is the Aramaic “Besiyata dishmaya” – with the help of Heaven. Some prefer בס״ד precisely because it does not contain a letter standing for God’s name.

Sources

וַיֹּאמֶר יִתְרוֹ בָּרוּךְ יְהוָה אֲשֶׁר הִצִּיל אֶתְכֶם מִיַּד מִצְרַיִם וּמִיַּד פַּרְעֹה אֲשֶׁר הִצִּיל אֶת־הָעָם מִתַּחַת יַד־מִצְרָיִם
Exodus 18:10

Talmud and halachic sources

Talmud, Pesachim 50a – pronouncing God's name
Talmud, Makkot 22a; Shevuot 35a – erasing God's name
Shulchan Aruch, Yoreh De'ah 276

Frequently asked questions

What does B”H mean at the top of a letter?: “Baruch Hashem” or “Be’ezrat Hashem” (with God’s help). BS”D means “with the help of Heaven” in Aramaic.
Why do Jews write G-d?: Out of respect, to avoid erasing or discarding God’s name. It is a custom; many authorities say the English word has no formal sanctity.
How is Baruch Hashem used in conversation?: As an answer to “How are you?” (“Baruch Hashem, good”), or to thank God when sharing good news.
What does Hashem mean?: “The Name” – a respectful way to refer to God in everyday speech.