It is a Dracaena marginata - Dragon Tree. The bad leaves you are seeing are either caused by the plant drying out, getting two wet, physical damage such as being knocked or bashed by something or cold damage. As it is in your house I doubt it is cold so probably one of the other three.
You can cut the leaves off quite far down near the stem. Check that the pot is not full of water as the container you have it in will not have drainage holes. Make sure it is not too dry by checking the compost has not left the sides of the pot. If you can see a gap down the side then it has dried out too much.