According to catholicism, what is the signification of burning incense during the liturgy? What is the signification of burning incense during mass and other liturgical functions?
One commentary on this survives from a time when the Roman Catholic Church was united with the eastern Sees.  It is from a work in Greek by Germanus I, Patriarch of Constantinople from 715 to 730, entitled Ecclesiastical History and Mystical Contemplation, available in a dual Greek-English format from St. Vladimir Seminary Press (Germanus is regarded as a Saint within both the Eastern Orthodox and Roman Catholic Churches).

Although he is explaining the eastern, Byzantine liturgical rite and not the western, I think that his explanation would also be accepted within the context of the Roman Catholic Mass:


  The censer demonstrates the humanity of Christ, and the fire His
  divinity.  The sweet-smelling smoke reveals the fragrance of the Holy
  Spirit which precedes.  For the censer denotes sweet joy.
  
  Again, the interior of the censer is understood as the [sanctified]
  womb of the [holy] virgin [and Theotokos] who bore the divine coal,
  Christ, in whom the whole fulness of deity dwells bodily (Col. 2:9).
  All together, therefore, give forth the sweet-smelling fragrance.  Or
  again, the interior of the censer points to the font of holy baptism,
  taking into itself the coal of divine fire, the sweetness of the
  operation of the Holy Spirit, which is the adoption of divine grace
  through faith, and exuding a good odor.