Lord Krishna eulogises the Cosmic Form because Arjuna should be regarded to have achieved all his ends by seeing this Cosmic Form. It is also an inducement to all spiritual aspirants to strive to attain this sublime vision. What they should do is explained by the Lord in verse 53 to 55.
Translation
11.47 The Lord said By My grace, O Arjuna this Supreme Form, luminous, universal, infinite, primal, never seen before by anyone but you, has been revealed to you through My own free will.
Meaning
Lord Krishna eulogises the Cosmic Form because Arjuna should be regarded to have achieved all his ends by seeing this Cosmic Form. It is also an inducement to all spiritual aspirants to strive to attain this sublime vision. What they should do is explained by the Lord in verse 53 to 55.
Word by word
मया by Me प्रसन्नेन gracious तव to thee अर्जुन O Arjuna इदम् this रूपम् form परम् supreme दर्शितम् has been shown आत्मयोगात् by My own Yogic power तेजोमयम् full of splendour विश्वम् universal अनन्तम् endless आद्यम् primeval यत् which मे of Me त्वत् from thee अन्येन by another न not दृष्टपूर्वम् seen before.