Q:

What is the meaning of word Sanskara?

Recently I participated in the Antim Sanskara of my Father in Law.
Also we say that " He or She is very Sanskari. "
In both the context word Sanskar is used.
My questions are : What is the meaning of the word Sanskara?
Do animals also have Sanskaras? 

A:

P.V Kane  - in his book History Of Dharmasastra Vol II Part I is quoting  the meaning of word samskara given by Sabara Swami in his commentary of Jaiminis Purva Mimansa sutras 1.1.3 and Kumarila Bhatta in Tantra-Vartika .

संस्कारो नाम स भवति यस्मिञ्जाते पदार्थो भवति योग्य : कस्य चिदर्थ स्य |
Sabara explains samskara as that which being affected makes certail
  thing or a person fit for certain purpose..

And Kumarila Bhatta in Tantra-Vartika (a commentary on Śabara's Bhāṣya on the Pūrvamīmāṃsā sūtras of Jaimini)  says that 

योग्यतां चादधाना: क्रिया : संस्कारा इत्युच्चते |
"Samskaras" are those actions and rites that impart fitness. Fitness
  is of two kinds ;it arises by removal of taints (sins) or by the
  generations of freash qualities.

see Point 448 & footnote on the page.

A:

There are many meanings for Sanskara or Saṃskāra (संस्कार):

putting together
making perfect
consecrations
behavioral traits
dispositions
accomplishing well

A Grihastha (householder) has 3 kinds of duties/rituals/consecrations:

Nitya (regular),

Naimaitik (causal) and

NityaNaimaitik (a combination of both). - Markandeya Purana

Most of the Samskaras from the list of 16 Samskaras (Ṣoḍaśa Saṃskāra) generally falls under Naimaitik (causal) rituals/consecrations category.
The sanskaras vary in number and details. They range from the list of 40 sanskaras in the Gautama Dharmasutra to 16 sanskaras in the Grhyasutra.
The behavioral traits such as compassion, patience, non-envy, purity of thought speech & body, inner calm & peace, positive attitude and generosity etc. also comes under Saṃskāras.

Antyesthi or Antim Sanskar (Cremation) is part of 16 Samskaras as disscussed here.

When someone says "He or She is very Sanskari"; they refer behavioral traits of a person such as compassion, patience, non-envy, purity of thought speech & body, inner calm & peace, positive attitude and generosity etc. which are included in 40 sanskaras. सदाचार (morality or good behavior
) is also closely related with the statement "He or She is very Sanskari".

