The NCBI web site is, in essence, a database of biological information. The areas of the web site I am most familiar with are to do with genetic information.

What can you find?
you can type in a name of any organism e.g. Human (Homo Sapien) or Rat (Rattus) and you can find all genetic sequencing information available.

You can look for a specific gene e.g. one coding for one or more specific enzymes. You can then cross check this against the organism and where in the genome it can be found.

What can you do with this information?
Now this depends on what you are trying to do (is this your job or your hobby?). It is an invaluable tool for anybody working in the field of genetics. All of the human genome sequenced to date (even unidentified bits) can be found here.

A major feature of the site is called "Blast", this compares a given DNA sequence with every single bit of DNA on the database (now however you look at it, that is huge) and gives you results in order of homology (most similar first)

This means you can take a known gene e.g. in a rat and run a search for all similar sequences, the chances are you will find lots of genes in different organisms e.g. human - but they are all the same gene just different, unidentified versions. As such, you can discover a new gene, before the experts do!!! This is due to the large amounts of genome sequencing been/being done (Human genome sequencing project is largely responsible for this), but as yet the functions of many of these genes are not known. If you think about it, it becomes obvious that future work in molecular biology will be aimed at gene function and protein regulation; gene sequencing is becoming old technology.