An idiomatic expression which refers to tests of your patience and endurance. The astute among you will notice that the expression encapsulates redundancy, since trials and tribulations are the same thing.
What might trials and tribulations entail in a practical sense? To get an idea, read a story about bureaucracy by Kafka - The Trial, say - or have a look at poor BaronCarlos' account of his employment as an an e-mail technical support representative. Oh dear.