To leave a print, impression, image, etc.
For a fee, they can imprint the envelopes with a monogram.
To learn something indelibly at a particular stage of life, such as who one's parents are.
To mark a gene as being from a particular parent so that only one of the two copies of the gene is expressed.
Any kind of phase-sensitive learning (learning occurring at a particular age or a particular life stage) that is rapid and apparently independent of the consequences of behavior.