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Natyashastra 

Mugdha (मुग्ध) or Mugdhanāyikā refers to a “tender, youthful, and young heroine”, of the Svakīya type and represents one of the three kinds of “heroines” (nāyikā) in a dramatic representation, according to the Abhinaya-sara-samputa, as used within the classical tradition of Indian dance and performance, also known as Bharatanatyam.—In the depiction of any mood or sentiment, a dance performance or a dramatic representation takes the medium of the hero (nāyaka) and the heroine (nāyikā). The heroine is called svakīya when she possesses good character and is upright. She is again classified into three types [viz., Mugdha-nāyikā].

The heroine of the Mugdha type is an adolescent and partly experienced. She possesses desire and shyness in equal measure and is intoxicated by her lover.

Shaktism (Shakta philosophy)

Mugdha (मुग्ध, “stunned”) refers to one of the sixty defects of mantras, according to the 11th century Kulārṇava-tantra: an important scripture of the Kaula school of Śāktism traditionally stated to have consisted of 125.000 Sanskrit verses.—Accordingly, as Īśvara says to Śrī Devī: “For those who do japa without knowing these defects [e.g., mugdha—stunned], there is no realization even with millions and billions of japa. [...] Oh My Beloved! there are ten processes for eradicating defects in Mantras as described. 

Also I am giving some reference about meaning of Mugdha in different dictionary settings.

In Sanskrit 

Mugdha (मुग्ध).—a. [muh-kta]

1) Stupefied, fainted.

2) Perplexed, infatuated.

3) Foolish, ignorant, silly, stupid; शशाङ्क केन मुग्धेन सुधांशुरिति भाषितः (śaśāṅka kena mugdhena sudhāṃśuriti bhāṣitaḥ) Bv.2.29; अयि मुग्धे काऽन्या चिन्ता प्रियासमागमस्य (ayi mugdhe kā'nyā cintā priyāsamāgamasya) V.3.

4) Simple, artless, innocent; अपूर्वकर्मचण्डालमयि मुग्धे विमुञ्च माम् (apūrvakarmacaṇḍālamayi mugdhe vimuñca mām) U.1.46; Māl. 7.1; दृष्टोत्साहश्चकितचकितो मुग्धसिद्धाङ्गनाभिः (dṛṣṭotsāhaścakitacakito mugdhasiddhāṅganābhiḥ) Me.14.

5) Erring, mistaken.

6) Attractive by youthful simplicity (not yet acquainted with love), child-like; (kaḥ) अयमाचरत्यविनयं मुग्धासु तपस्विकन्यासु (ayamācaratyavinayaṃ mugdhāsu tapasvikanyāsu) Ś.1.24; U.6.35; R.9.34.

7) (Hence) Beautiful, lovely, charming, pretty; हरिरिह मुग्धवधूनिकरे विलासिनि विलसति केलिपरे (haririha mugdhavadhūnikare vilāsini vilasati kelipare) Gīt.1; U.3.5.

8) New (as the moon); मालतीनयनमुग्धचन्द्रमाः (mālatīnayanamugdhacandramāḥ) Māl.9.21. (com. bālacandraḥ).

-gdhā A young girl attractive by her youthful simplicity, a pretty young maiden; (regarded as a variety of Nāyikā in poetic compositions); काचं मणिं काञ्चनमेकसूत्रे मुग्धा निबध्नन्ति किमत्र चित्रम् (kācaṃ maṇiṃ kāñcanamekasūtre mugdhā nibadhnanti kimatra citram) Udb.

Source: Cologne Digital Sanskrit Dictionaries: Shabda-Sagara Sanskrit-English Dictionary

Mugdha (मुग्ध).—mfn.

(-gdhaḥ-gdhā-gdhaṃ) 1. Lovely, beautiful. 2. Stupid, ignorant, an idiot, a fool. 3. Simple, silly. 4. Infatuated. f.

(-gdhā) A young and lovely female. E. muh to be foolish, aff. kta, deriv. irr.

--- OR ---

Mugdhā (मुग्धा).—f.

(-gdhā) A girl attractive by her artlessness, (in rhetoric.)

Source: Cologne Digital Sanskrit Dictionaries: Cappeller Sanskrit-English Dictionary

Mugdha (मुग्ध).—[adjective] stupefied, perplexed; gone astray, lost; foolish, silly; careless, innocent, charming, lovely.

Source: Cologne Digital Sanskrit Dictionaries: Monier-Williams Sanskrit-English Dictionary

1) Mugdha (मुग्ध):—a etc. See p. 825, col. 1.

2) [from muh] b mfn. gone astray, lost, [Ṛg-veda; Vājasaneyi-saṃhitā]

3) [v.s. ...] perplexed, bewildered, [Atharva-veda; Daśakumāra-carita]

4) [v.s. ...] foolish, ignorant, silly, [Śatapatha-brāhmaṇa] etc. etc.

5) [v.s. ...] inexperienced, simple, innocent, artless, attractive or charming (from youthfulness), lovely, beautiful, tender, young ([especially] ā f. a young and beautiful female, often in [vocative case]; also in [rhetoric] a variety of the Nāyikā), [Kāvya literature; Kathāsaritsāgara; Rājataraṅgiṇī]

6) [v.s. ...] (ifc.) strikingly like, [Vikramāṅkadeva-carita, by Bilhaṇa; Bālarāmāyaṇa]

Source: Cologne Digital Sanskrit Dictionaries: Yates Sanskrit-English Dictionary

Mugdha (मुग्ध):—[(gdhaḥ-gdhā-gdhaṃ) a.] Stupid, a fool; infatuated; beautiful.

Source: DDSA: Paia-sadda-mahannavo; a comprehensive Prakrit Hindi dictionary (S)

Mugdha (मुग्ध) in the Sanskrit language is related to the Prakrit words: Gummia, Muḍḍha, Muddha, Muddhā.

In Marathi language 

mugdhā (मुग्धा).—f S A female not arrived at puberty, a girl under sixteen years of age, a maid. See bālā & prauḍhā.

in Hindi Language 

1) Mugdha (मुग्ध) [Also spelled mugdh]:—(a) infatuated; charmed, under a spell; attracted (towards); ~[kara/kārī] charming, that which casts a spell or causes infatuation, attractive.

2) Mugdhā (मुग्धा):—(a and nf) according to traditional Indian Poetics, a simple, innocent and artless heroine within whose person youth has just been ushered.

There is one more word related to Mugdha , Mugdhabhava: 

Mugdhabhāva (मुग्धभाव).—simplicity, silliness.

Derivable forms: mugdhabhāvaḥ (मुग्धभावः).

Mugdhabhāva is a Sanskrit compound consisting of the terms mugdha and bhāva (भाव).

In kannada language 

Mugdhabhāva (ಮುಗ್ಧಭಾವ):—[noun] the quality or state of being innocent; freedom from sin or moral wrong.