Definitions: praṇam

[yajvan]

praṇam प्रणम् some write praṇām प्रणाम्

• praṇam is defined as to bend or bow down before. We can see this from its components:
  • pra is forward , in front , on , forth; mostly in connection with a verb of motion which is often to be supplied ; sometimes repeated before the verb
  • ṇam= nam , meaning to turn towards, to aim at, to yield or give way , keep quiet or be silent

Discussion
This pra-ṇam is rooted in nam - bending or bowing before. One is making obeisance i.e. a movement of the body expressing deep respect or courtesy, as before a superior.

Other views, not different, just extensions on the theme suggests the following:
nam is also defined as to yield or submit . But what is being submitted? pra. What of this pra? It is rooted in pṝ or prā which means filling , fulfilling .
Now what do we have? prā-nam - I am submitting or yielding the fullness in me ( to you). Some view it as I am submitting myself to the fullness in you.

What of pra-ṇa-m ? We look to this sound ṇa. It has several meanings, one of them is gift. Now we have, I give forth (pra) + a gift (ṇa).
Gifting is quite approprite and is dharmic in nature - so says the Mahābhārata, santi parvan. But what is one giving then with a bow?
They are offering the fullness ( bhuman) in themsleves to the fullness in the other. 'Other' here is the devatā, guru, master, mother, father, superior, etc.

Others can see this ṇa as negation i.e. not 'me'. Then who ? this ṇa is a noun for śiva; it is also another name/sound for nirvṛti meaning complete satisfaction or happiness , bliss , pleasure , delight and associated with kriṣṇa ( some prefer it written kriṣṇ ). Then we have I bow down (delightfully) before śiva or kriṣṇ in you.

What of this praṇa-m ? praṇa ( not prāṇa or breath of life, or life force) means ancient , old . We find this sound-form in purāṇa, belonging to ancient or olden times , ancient , old.
What is ancient in you , or in the other person, devatā, or superior, one may be bowing to? The Supreme, some may call puruṣa. This puruṣa is rooted in pṛ to protect escue , save , protect , escort. That ancient One, that is Supreme and in all, we are bowing to Him, the One.


References
A Concise Dictionary Of Indian Philosophy -John Grimes
Monier Williams Sanskrit-English Dictionary (2008 revision)
general studies & knowledge