श्रीकान्तो (shrIkAnto) ...

श्रीकान्तो मातुलो यस्य​
जननी सर्वमंगला।
जनकः शंकरो देवः
तम् वन्दे कुंजराननम्॥

shrIkAnto mAtulo yasya
jananI sarva mangalA |
janakah shankaro devah
tam vande kunjarAnanam ||

श्रीकान्तो  - refers to Lord Maha Vishnu
मातुलो  यस्य​ - whose maternal uncle is
जननी  - mother
सर्वमंगला - the auspiciousness of all auspiciousness (refers to Goddess Parvati)
जनकः - father
शंकरो देवः - Lord Shiva
तम्  - Him
वन्दे  - worship
कुंजराननम् - One with an elephant face (कुंजरः is another word for elephant)

The word श्री represents respect, esteem, wealth, fortune etc. and is a reference to Goddess Lakshmi. The word कान्तः means husband. Hence, the word श्रीकान्त: refers to Lord Maha Vishnu. Similarly, the word शंकर​ comes from शंक + हर​. The word शंक refers to doubt and the word हर​ means to destroy. Faith is the absence of all forms of doubt. Faith is a natural expression of the Sattvic nature in man.

The nature of man can be such that either of the 3 qualities - Sattva, Rajas or Tamas - can dominate. Sattva refers to immense internal bliss and complete surrender, Rajas refers to passion in or for work, emotion, wealth etc. and Tamas refers to complete ignorance and wickedness. While the qualities of rajas and tamas are ego oriented and tend to strengthen the egoism in us, the quality of sattva inspires us to surrender to the divine and work for our salvation from the cycle of births and deaths. Selflessness, humility, purity of thought and devotion are its fundamental characteristics. Without these qualities, man cannot expect to progress much on the spiritual path. Shankara destroys the animal nature in man, which is represented by the tamasic and rajasic qualities. These two qualities are primarily responsible for his lower nature, his egoistic disbeliefs and profound ignorance. By destroying these qualities and thereby our lower nature, Siva establishes the conditions conducive to the emergence of divine nature in man. It is interesting to note that in the Hindu mythology, most of the demons, such as Ravana of the Ramayana or Bhasmasur and many others, were great devotees of Siva, who despite of their excessive wickedness, showed immense faith in Siva. These stories tend to suggest that only Siva can transform such individuals, who are characterized by excessive rajas and tamas, through His immense powers. The moral of these stories is that if you have excessive rajas and tamas in you, you should invariably worship Lord Siva in order to overcome these  impediments. This, in essence, is the meaning of the word Shankara, the Destroyer of all doubts.

Without further ado, the gist of the Sloka is:
One whose maternal uncle is Lord Maha Vishnu, One whose mother is the representation of all things auspicious, One whose father is Lord Shiva, I worship Him, the elephant-faced One.