The man was either very shy or very excited in Mary's presence. It implies that she was sheltered from men in her upbringing or she was socially inept.

to rear = 饲

bred

We use 'rear' to mean to bring a person from child to maturity through care and education ( bring up, raise). 'They reared five children.' 'Reared' in your sentence is a past participle used as an adjective to modify 'lady' ( a lady who was brought up in the way Mary was) Mary was probably very well brought up and educated and he found it difficult to find things to talk to her about.

'reared' means 'being brought up' as Mary was. The way she was 'raised' or 'educated' as well.