Monastic means like in a monastery. So what is it like in a monastery? Well, it's solitary, somewhat isolated, plain, and disciplined. If you take monastic vows, you promise to live this way.
Being monastic might sound like a strange or a hard thing to be, but you can compare it to student life very well. Both monks and students spend a lot of time studying books. Monks like quiet, and students need quiet to get work done. Monks live in a community devoted to religion, and students study in a community devoted to learning. The stereotypical party lifestyle of a student isn't very monastic though.