Why is bioinformatics important?

Same reason any statistics is important. There is a lot of data to sift through so you invent tools to sift through that data for you.

If you have a genome form some organism that is 2 million bases and you are trying to annotate the genes it would take a long time to do this manually. To avoid this you write software or code your own program that will look at the letters and find an ATG (start) and TAG (stop) and annotate that gene for you.

A bit more complex than that and there other examples but that's basically it. There is too much data to look though on your own so you make computers do it for you.