What is this shell/Bash syntax: someVariable=someValue someCommand

This is equivalent to:

( export someVariable=something; command )

This makes someVariable an environment variable, with the assigned value, but only for the command being run.

Here are the relevant parts of the bash manual:

Simple Commands

A simple command is a sequence of optional variable assignments followed by blank-separated words and redirections, and terminated by a control operator. The first word specifies the command to be executed, and is passed as argument zero. The remaining words are passed as arguments to the invoked command.

(...)

Simple Command Expansion

If no command name results [from command expansion], the variable assignments affect the current shell environment. Otherwise, the variables are added to the environment of the executed command and do not affect the current shell environment.

Note: bear in mind that this is not specific to bash, but specified by POSIX.

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Edit - Summarized discussion from comments in the answer

The reason BAZ=JAKE echo $BAZ, doesn't print JAKE is because variable substitution is done before anything else. If you by-pass variable substitution, this behaves as expected:

$ echo_baz() { echo "[$BAZ]"; }
$ BAZ=Jake echo_baz
[Jake]
$ echo_baz
[]

These are variable assignments in the context of simple commands. As xhienne has mentioned, for external commands they are equivalent to exporting the assigned value(s) for the duration of the command.

In your examples you're using a built-in command, so the behaviour isn't quite the same: the assignments affect the current environment, but whether the effect lasts after the execution of the built-in command is unspecified. To understand your examples, you need to know that parameter expansion happens before variables are handled; thus with

 BAZ=jake echo $BAZ

the shell first expands $BAZ (resulting in nothing), then sets BAZ to jake, and finally runs

 echo

which prints an empty line. (Then the shell forgets BAZ as your subsequent echo $BAZ shows.)

 BAZ=jake; echo $BAZ

is interpreted as two commands: first the BAZ variable is set in the current environment, then echo $BAZ is expanded to echo jake and executed.

There are a few key things that happen here:

• As explained in bash reference manual, Simple Command Expansion, section "If no command name results, the variable assignments affect the current shell environment. Otherwise, the variables are added to the environment of the executed command and do not affect the current shell environment." Thus, when you say var="something" command arg1 arg2, the command will run with var being in command's environment and disappearing after command exits. Demonstration of this is simple - access the command's environment from within the command:

  $ BAZ="jake" python -c "import os; print os.environ['BAZ']"                                                              
  jake
  

  This is nothing to be surprised about. Such syntax is frequently used to run programs with modified environment. My fellow unix.stackexchange.com and askubuntu.com users will recognize this example: if user uses German locale, and you only speak in English, you can ask them to reproduce whatever issue they're having and obtain output in English like so:

  LC_ALL=C command
  

  Note also that environment access isn't specific to python. It can be done with C or any other programming language. It just so happened to be my "weapon of choice" right now and only used for this demo.

• The variable expansion occurs before anything runs. Thus, when you run something like BAZ="foo" echo $BAZ, the shell looks into its environment first, finds no variable BAZ there , and thus leaves $BAZ empty. Simple demonstration of that is:

  $ BAZ="jake" python -c "import sys; print 'ARG:',sys.argv[1]" $BAZ                                                       
  ARG:
  Traceback (most recent call last):
    File "<string>", line 1, in <module>
  IndexError: list index out of range
  

It's important to also note, the distinction from BAZ=jake; echo $BAZ which is two separate command statements and here BAZ=jake will stay in shell's environment. The use case depends on your intentions. If you intend running more than one program that needs such variable, it might be desirable to export such variable. If you only need it for this one specific time, then preceding variable assignments are might be preferable.