In Judaism, it's permissible for men to pray on their own, but it's considered truly sacred to pray in a public environment as part of a minyan. 

Meaning

Minyan (plural, minyanim) literally means "count" and refers to a quorum of 10 men required for any public prayer gathering. A minyan's 10 men comprises individuals older than bar mitzvah age, or 13 years. 

Origins

The rabbis believed that wherever 10 Israelites are gathered, whether for worship or studying Torah, the divine presence (Shekinah) dwells among them.

 The concept of a minyan finds its beginnings in the Mishnah in Megillah: 

"They do not [1] 'divide' over the Shema' [Hear, O Israel], [2] nor pass before the Ark, [3] nor lift their hands, [4] nor read from the Law, [5] nor conclude with the Prophets, [6] nor arrange the standing and sitting, [7] nor say the benedictions of the mourners or the consolation of the mourners, [8] nor the benedictions of the bridegrooms, [9] nor use God's name in preparing for grace after meals, with fewer than ten."

?The Babylonian Talmud states that this ruling derives from Numbers 14:27, in which 12 spies are sent out to scout the land of Canaan and report back whether the land is conquerable. Ten of the spies returned with negative reports, saying that the land could not be conquered. Joshua and Caleb, on the other hand, remained faithful that the land could be conquered and were subsequently rewarded in many ways. 

Numbers reports that God was disappointed with the 10 spies and says to Moses and Aaron, "How long will this evil assembly provoke [the Jewish nation] to complain against me?" Thus, from here the rabbis understood that an "assembly" comprises 10 men.

 

Who Counts?

As mentioned, all Jewish men of bar mitzvah age (13) or older are considered to be eligible to count in a minyan. A minyan is required for the recitation of many instances, including

• Any public worship that includes kaddish, barechu, and kedusha. 
• Reading from the Torah and prophets with blessings.
• The blessings read at a wedding or during the ?sheva brachot. 
• Recitation of the priestly blessing (?birkat ha'kohanim).
• ?Recitation of certain prayers of thanksgiving (birkat ha'gomel).
• Recitation of the Thirteen Attributes of Mercy.

There are leniences when it comes to the creation of a minyan regarding minors. For example, in some communities, nine men and a boy older than 12 years of age will count as a minyan, while in other cases a minor as young as 6 years of age might be counted in a minyan. (For more minors counting in a minyan, read Aharon Ziegler's "Counting a Minor in a Minyan". Halakhic positions of Rabbi Joseph B. Soloveitchik: Volume III, 2004.)

All members of the minyan must be in the same room to count as a whole quorum, although there is a discussion by Maimonides that says in a small space the 10 men can be in two adjoining rooms without upsetting the minyan but that they must be able to hear each other. 

The role of the minyan in Judaism offers a potent lesson of the role of community and how every individual has the ability to serve a purpose greater than himself. 

Women

In Orthodox Judaism, a woman cannot be counted in a minyan. However, much of what Orthodox Judaism understands and practices by way of prayer derives from the prayers of Chana, a woman, thousands of years ago. However, there is a move to create women's tefillah (prayer) groups within Orthodox Judaism. 

Reform Judaism declared women to count in a minyan in 1845 at the Frankfort Synod, which formalized the custom for women dating back to 1811. 

Women and men were officially counted as equal for a minyan as announced by the 1973 Committee on Jewish Law and Standards of Conservative Judaism. 

For more on women in Jewish law, read Rachel Biale's Women and Jewish Law: The Essential Texts, Their HIstory, & Their Relevance for Today.