Ndtyhij

Generally, Hindus are vegetarian. They avoid mamsah i.e flesh of animals like meat, fish - because it means their suffering and death. Some avoid eggs also. Atleast it is very limited, and they don't eat it daily like western countries, and avoid it during religious functions.

What is the reason behind this ? Is compassion/ahimsa the only reason ? Is it voluntary or compulsory ?

Is there any punishment for eating meat ? Is there any reward for avoiding meat ?
What is the real meaning of the word 'mamsah' (मांसः)? Does it have anything to do with why they are vegetarian ?

Eating meat outside of rituals is considered as a sin unanimously in all scriptures.. that's why probably.

Manu Smriti 5.31. ’The consumption of meat (is befitting) for
sacrifices,’that is declared to be a rule made by the gods; but to
persist (in using it) on other (occasions) is said to be a proceeding
worthy of Rakshasas

5.33. A twice-born man who knows the law, must not eat meat except in conformity with the law; for if he has eaten it unlawfully, he will,
unable to save himself, be eaten after death by his (victims)

5.48. Meat can never be obtained without injury to living creatures, and injury to sentient beings is detrimental to (the attainment of)
heavenly bliss; let him therefore shun (the use of) meat.

Also abstaining from eating meat bestows spiritual benefits.

5.56. There is no sin in eating meat, in (drinking) spirituous liquor, and in carnal intercourse, for that is the natural way of
created beings, but abstention brings great rewards.

As for punishments, we have the following Manu Smriti verse:

5.38. As many hairs as the slain beast has, so often indeed will he who killed it without a (lawful) reason suffer a violent death in
future births.

Without lawful reason -- that is killing animals outside of rituals.

For your query about the word Mamsah see the following:

5.55. ’Me he (mam sah)’will devour in the next (world), whose flesh I eat in this (life); the wise declare this (to be) the real meaning of
the word ’flesh’(mamsah).

Manu Smriti:

'Me he (mam sah)' will devour in the next (world), whose flesh I eat
in this (life); the wise declare this (to be) the real meaning of the
word 'flesh' (mamsah).

He who permits (the slaughter of an animal), he who cuts it up, he who kills it, he > who buys or sells (meat), he who cooks it, he who serves it up, and he who eats it, (must all be considered as) the slayers (of the animal).

He who during a hundred years annually offers (Ashvamedha), and he who entirely abstains from meat, obtain the same reward for their meritorious (conduct).