Please explain the meaning of "equal protection of the laws" in American Government.

The Fourteenth Amendment to the U.S. Constitution includes
the so called, “Equal Protection Clause” which provides that states may not deny people
the equal protection of the laws.  The practical effect of this has been not the
outright abolition of any law that treats different people differently, but rather to
expose such laws to judicial scrutiny which may then lead to a declaration that they are
unconstitutional and therefore, void. 

The court has given
rise to different levels of scrutiny that will be applied when a law appears to violate
the equal protection clause.  Laws which treat people differently on the basis of race,
religion, or national origin, or which burden fundamental rights, receive the highest
level of judicial scrutiny.  These are almost always struck down.  Laws which treat
people differently because of gender or illegitimacy receive slightly lower levels of
scrutiny.  There are, after all, real and legitimate differences between men and women
and the government may well have valid reasons for wanting to treat people differently
based upon these differences (for example, a major division in the way laws treat men
versus women may be based upon the fact that only women are capable of becoming
pregnant.)

Finally, the lowest level of scrutiny relates to
laws which treat people differently but do not do so on the basis of one of the suspect
classes (race, religion, national origin, gender, etc.) and do not burden fundamental
rights.  This lowest level of scrutiny demands only that the government advance some
rational basis for the law at issue.  This "rational basis" scrutiny is historically
easy to defend against, but the government will not always be successful.  For example,
if a state cannot prove that its anti-sodomy law has any basis other than an irrational
fear and hatred of homosexuals, that law will not pass even the rational basis
test.