Tax Classes determine which rate your income is taxed at. From Wikipedia, this is how your Tax Class is determined in Germany.
class 1 = single, living in a registered civil partnership, divorced, widowed or married, unless they fall under tax category 2, 3 or 4.
class 2 = single but is entitled to single parent allowance.
class 3 = married and spouse does not earn wages, or the spouse earns a wage but is classified under tax category 5 by request of both spouses, or to widowed workers for the calendar year following that of the spouse' death if both were residing in Germany and were not separated on the day of the spouse's death.
class 4 = married, both spouses earn a wage, reside in Germany, and are not separated.
class 5 = married but one of the spouses, at both spouses' request, is classified under tax category 3.
class 6 = workers receiving multiple wages from more than one employer, in order for wage tax to be withheld for the second and any additional employment contracts.The taxation at source for capital income will be done with a flat tax rate of 25% (add solidarity surcharge of 5.5% of the amount of tax and, if applicable, church tax).