There are many meanings for Sanskara or Saṃskāra (संस्कार):
A Grihastha (householder) has 3 kinds of duties/rituals/consecrations:
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".