he is a throughbred boxer with an outstanding pedigree.
A boxer is a breed of dog. A thoroughbred with an outstanding pedigree means the dog is pure boxer, and his blood lines can be traced back several generations.
he's got a taste fo exotic pets.
Exotic pets are considered to be animals like monkeys, certain lizards, snakes, or even wild animals (like lions and bears). "He has a taste for exotic pets" means he prefers to own these types of animals instead of a dog or cat.
she strode off down the resturatnts with thoms following close at her heels .
"Strode" is the past tense of "stride," which means to take long, confident steps. She left the restaurant walking in a hurry, as if she had somewhere important to go, and Thomas walked quickly behind her, trying to keep up with her pace.