That is, you should, unless you already know the difference between Sunni and Shia.
The summary: Islam’s Whittenberg Door moment came when Muhammad died; the issue was not faith vs. works but instead one of sucession.
The more “orthodox” view, held by Sunnis — who comprise by far the largest chunk of Muslims worldwide — is that Abu Bakr, a relative and early convert, is the rightful heir to the Prophet. This was a big deal politically as well as spiritually. Muhammad had a close relationship with Bakr, and frequently asked him to lead prayers in his absence, and furthermore was selected by a large group of Muslims upon the Prophet’s death (at Medina, in 632), which gives credence to this view. About ninety percent of Muslims are Sunni.
There were, of course, those who refused to accept Bakr, and who instead supported Ali ibn Abi Talib, also a relative of the Prophet (and also his son-in-law). Complicating matters is that Ali did eventually become Caliph (the 4th), but this doesn’t seem to mollify the Shia. To them, he’s the first Imam, as opposed to the last of the Four Rightly Guided Caliphs (as he is to Sunnis). Shia have a significant majority only in Iran and Iraq.
The divide was sufficiently far back that oral tradition has produced different traditions and spiritual laws as well as titles; Ayatollah is a Shia role, for example (apparently).
All this matters for lots of reasons, but one big damn deal to take note of is the fact that the Taliban and Osama are fundamentalist Sunnis, not Shia.