These are popular web sites, each of which contain millions of records that are of interest to genealogists.
FamilySearch.org is a free site that is made available by the LDS Church (i.e., the Mormons).   No credit card or religious affiliation is required but you will be required to create a free account in order to access the site.  Its databases contain records from around the world, including vital records, census records, immigration records, family trees, military records, and newspapers, among many others.  Since it is free, it is the starting point for many researchers.  Other sites have some important advantages over it, however, so it should not be used exclusively.
Ancestry.com is a commercial website with a similarly-wide variety of records types, including many unique databases and some which overlap with FamilySearch.  Most indexes on Ancestry.com are free but to see the full record, one must have a subscription.
Fold3.com specializes in military records, including many original records that were digitized in partnership with NARA and are not available anywhere else.  Fold3.com is owned by Ancestry.com.  Like its parent company, the indexes on Fold3 can be accessed for free but you need a subscription to see the full record.  If you purchase a subscription to Ancestry.com, you can get a discounted upgrade to include Fold3.com.
NOTE: Don't make the mistake of dismissing Ancestry.com and Fold3.com on the grounds that they are paid subscription services. They contain important data types that are not available anywhere else and there are lots of ways for you to access them for FREE as described here.