Get Description of Emoji Character

Martin R's answer using Core Foundation's CFStringTransform() still works, but the key feature actually comes from kCFStringTransformToUnicodeName, and in Swift 2 we can use it simply like this, by bridging with NSString and calling stringByApplyingTransform:

let c: Character = "😄"
if let result = (String(c) as NSString)
    .stringByApplyingTransform(
        String(kCFStringTransformToUnicodeName),
        reverse: false) {
    print(result)
}

\N{SMILING FACE WITH OPEN MOUTH AND SMILING EYES}

The same for a String:

let s: String = "This is a 😄"
if let result = (s as NSString)
    .stringByApplyingTransform(
        String(kCFStringTransformToUnicodeName),
        reverse: false) {
    print(result)
}

This is a \N{SMILING FACE WITH OPEN MOUTH AND SMILING EYES}

The Core Foundation function CFStringTransform() has transformations that determine the Unicode standard name for special characters. Example:

let c : Character = "😄"

let cfstr = NSMutableString(string: String(c)) as CFMutableString
var range = CFRangeMake(0, CFStringGetLength(cfstr))
CFStringTransform(cfstr, &range, kCFStringTransformToUnicodeName, false)
print(cfstr)

Output:

\N{SMILING FACE WITH OPEN MOUTH AND SMILING EYES}

See http://nshipster.com/cfstringtransform/ for more information about CFStringTransform().

With Swift 5, you can use one of the two following ways in order to get the description of an Emoji character.

---

#1. Using Unicode.Scalar.Properties's name property

Unicode.Scalar.Properties has a name property. name has the following declaration:

var name: String? { get }

The published name of the scalar.

The Playground code sample below shows how to use name in order to get the published name of a Unicode scalar:

let emoji: Character = "😄"
for scalar in emoji.unicodeScalars {
    print(scalar.properties.name)
}

/*
 prints: Optional("SMILING FACE WITH OPEN MOUTH AND SMILING EYES")
 */

---

#2. Using Unicode.Scalar.Properties's nameAlias property

Unicode.Scalar.Properties also has a property called nameAlias with the following declaration:

var nameAlias: String? { get }

The normative formal alias of the scalar. [...] The nameAlias property is provided to issue corrections if a name was issued erroneously. For example, the name of U+FE18 is “PRESENTATION FORM FOR VERTICAL RIGHT WHITE LENTICULAR BRAKCET” (note that “BRACKET” is misspelled). The nameAlias property then contains the corrected name.

The Playground sample codes below show the difference between name and nameAlias for U+FE18 Unicode scalar:

let emoji: Character = "\u{FE18}" // ︘
for scalar in emoji.unicodeScalars {
    print(scalar.properties.name)
}
/*
 prints:
 Optional("PRESENTATION FORM FOR VERTICAL RIGHT WHITE LENTICULAR BRAKCET")
 */

let emoji: Character = "\u{FE18}" // ︘
for scalar in emoji.unicodeScalars {
    print(scalar.properties.nameAlias)
}
/*
 prints:
 Optional("PRESENTATION FORM FOR VERTICAL RIGHT WHITE LENTICULAR BRACKET")
 */

Swift 3 version of Eric Aya's answer:

let s = "This is a 😄"

if let result = s.applyingTransform(
    kCFStringTransformToUnicodeName as StringTransform,
    reverse: false) {
    print(result)
}

This is a \N{SMILING FACE WITH OPEN MOUTH AND SMILING EYES}