Your example is not about anonymous functions. It is about { and } which are not needed if there is only a single expression between them.
- An expression can be longer than a line.
- On a line there can be more than one expression (separated by semicolon).
- An anonymous function is not restricted to one line.

You can find the documentation for { as usual: help('{')

Examples:

x <- 3; y <- 4; z <- x + y  # more than one expression on a line

z <- x +
y +
2  # the expression x+y+2 extends over three lines

x <- matrix(1:30,3)
apply(x, 1, function(x) sd(x)/
median(x)) # anonymous function definition on two lines

Sometimes one has to be careful about linebreaks in the code. In some situation they are recognized as end of the syntactical unit by the interpreter. "be careful" in this situations mean:
Give the interpreter a reason to search on the next line.
This will not work:

x <- 11:15
x
[3]  # because of the linebreak it is not x[3]

But this will do:

x[
3
]
# the interpreter was searching for the ']' (till it was found)

This is the situation in which I learned my lesson:

if (...) { ... }
else { ... }     # unexpected 'else' !!!

From that time on I am coding this way:

if (...) {
   ...
} else {
   ...
}

See Unexpected 'else' in "else" error

A nonanonymous function (i.e. a named function) is nothing else than a function definition connected with an objectname by assignment:

fname <- function(...) ...

for later reuse. You can even do it in places where normally an anonymous function can be found:

x <- matrix(1:30,3)
apply(x, 1, FUN=(mysuperfunc <- function(x) sd(x)/median(x)) ) 

but this is the same with better readability:

mysuperfunc <- function(x) sd(x)/median(x)
x <- matrix(1:30,3)
apply(x, 1, FUN=mysuperfunc)