Sudoku is a number puzzle where the objective is to fill every row, column and box (3x3 grid) with the numbers from 1-9. Each unit (row, column or box) must have each number exactly once. The game starts with a number of fields pre-filled. Your objective is to fill the rest of the fields without breaking the constraints that each number can only be once in each row, column and box.
The basic gameplay, which will be enough to solve many easy Sudoku puzzles, is simply to look at an empty field and eliminate all numbers that are already present in the row, column and box it belongs to. In many cases this will be enough to find the correct number. And of course as soon as you've found the right number for one field, it will be easier to figure out other fields in the same row, column or box.
When you get into more difficult situations there are a number of different strategies you can use. The excellent page Sudoku Dragon has a good strategy page that covers many basic strategies as well as some advanced ones.