I’ll go from high-level down to your particular problem:

How Clojure (or LISPs) Generally Work

REPLs, or Read-Eval-Print Loops are the core of how LISPs are designed:

• The reader converts a stream of characters into data structures (called Reader Forms).
• The evaluator takes collection of reader forms and evaluates them.
• The printer emits the results of the evaluator.

So when you enter text into a REPL, it goes through each of these steps to process your input and return the output to your terminal.

Reader Forms

First some, clojure reader forms. This will be extremely brief, I encourage you to read or watch (part 1, part 2) about it.

A symbol in clojure is form that can represent a particular value (like a variable). Symbols themselves can be pass around as data. They are similar to pointers in c, just without the memory management stuff.

A symbol with a colon in front of it is a keyword. Keywords are like symbols with the exception that a keyword’s value are always themselves – similar to strings or numbers. They’re identical to Ruby’s symbols (which are also prefixed with colons).

A quote in front of a form tells the evaluator to leave the data structure as-is:

user=> (list 1 2)
(1 2)
user=> '(1 2)
(1 2)
user=> (= (list 1 2) '(1 2))
true

Although quoting can apply to more than just lists, it’s primarily used for lists because clojure’s evaluator will normally execute lists as a function-like invocation. Using the ' is shorthand to the quote macro:

user=> (quote (1 2)) ; same as '(1 2)
(1 2)

Quoting basically specifies data structure to return and not actual code to execute. So you can quote symbols which refers to the symbol.

user=> 'foo ; not defined earlier
foo

And quoting is recursive. So all the data inside are quoted too:

user=> '(foo bar)
(foo bar)

To get the behavior of (foo bar) without quoting, you can eval it:

user=> (eval '(foo bar)) ; Remember, foo and bar weren't defined yet.
CompilerException java.lang.RuntimeException: Unable to resolve symbol: foo in this context, compiling:(NO_SOURCE_PATH:1)
user=> (def foo identity)
#'user/foo
user=> (def bar 1)
#'user/bar
user=> (eval '(foo bar))
1

There’s a lot more to quoting, but that’s out of this scope.

Requiring

As for require statements, I’m assuming you found the former in the form of:

(ns my.namespace
    (:require [clojure.set :as set]))

ns is a macro that will transform the :require expression into the latter form you described:

(require '[clojure.set :as set])

Along with some namespacing work. The basics are described when asking for the docs of ns in the REPL.

user=> (doc ns)
-------------------------
clojure.core/ns
([name docstring? attr-map? references*])
Macro
  Sets *ns* to the namespace named by name (unevaluated), creating it
  if needed.  references can be zero or more of: (:refer-clojure ...)
  (:require ...) (:use ...) (:import ...) (:load ...) (:gen-class)
  with the syntax of refer-clojure/require/use/import/load/gen-class
  respectively, except the arguments are unevaluated and need not be
  quoted. (:gen-class ...), when supplied, defaults to :name
  corresponding to the ns name, :main true, :impl-ns same as ns, and
  :init-impl-ns true. All options of gen-class are
  supported. The :gen-class directive is ignored when not
  compiling. If :gen-class is not supplied, when compiled only an
  nsname__init.class will be generated. If :refer-clojure is not used, a
  default (refer 'clojure) is used.  Use of ns is preferred to
  individual calls to in-ns/require/use/import:

REPL usage

In general, don’t use ns in the REPL, and just use the require and use functions. But in files, use the ns macro to do those stuff.