This website offers complex pedigree reports and knowing how to read them and understanding what everything means in a pedigree can really help you out. If you scroll to the bottom of this page, you'll find the pedigree for Kentucky Derby winner REAL QUIET. We'll be using this pedigree as an example so you can follow along.
Inbreeding occurs in a pedigree when the same horse appears twice through different offspring. Real Quiet's pedigree has a fair amount of inbreeding in it. The Pedigree Database will show inbred horses by placing a colored bar to the right of names inside the pedigree. Notice in Real Quiet's pedigree below that there are colored bars next to Dr. Fager, Raise a Native, Cequillo, and Rough'n Tumble. The bars are color coded so that you can quickly find matching sets of horses. All of these horses appear more than once in the pedigree through different offspring, notice that Aspidistra also appears more than once in the pedigree, yet she doesn't have a colored bar next to her name. This is because she only appears through her son Dr. Fager and no other horses.
Inbred horses that appear in both the dam and sire side of the pedigree are referred to as cross duplicates. In Real Quiet's pedigree, Raise a Native appears twice, once in Quiet American's pedigree and once in Really Blue's pedigree. Dr. Fager on the other hand only appears in Quiet American's pedigree and thus he isn't a cross duplicate.
In thoroughbreds, there are three types of siblings that are generally noted. Full siblings (full brothers/sisters that share the same sire & dam). 3/4 siblings (horses that share 3 out of 4 grandparents). In Real Quiet's pedigree, Dumure and Killaloe are 3/4 siblings sharing Rough'n Tumble, Aspidistra, and Cequillo. Half siblings are those that either share two grandparents or have the same dam. In Real Quiet's pedigree, Quiet Charm and Grand Splendor share the same dam and are thus considered half siblings. Note that horses that share the same sire are not generally considered half siblings. In the pedigree database, the relationships will be noted by color coded dotted, dashed, and solid lines below a horse's name. A solid line will highlight full siblings, a dashed line (like the green one below Demure's name) shows 3/4 siblings. Dotted lines like the one below Quiet Charm show half siblings.
In the pedigree database, horses that have either won a grade I race or the equivalent of a grade I race (before the grading system came out) are always noted in bold text. Generally speaking, the more Grade I winners/champions in a pedigree, the better bred a horse is, especially when they show up in the dam's side of the pedigree. Note that most sires today have had fairly succesful racing careers and are often Grade I winners. It's not uncommon to see a good sire in a pedigree, but it's a lot less common to find mares who have done well.
Many horses in the database will show up with a career racing record and earnings next to their names. For instance Really Blue has the following numbers under her name. "21-3-5-1 $31,920". This means that she raced 21 times in her career, won 3 races, finished second 5 times and third 1 time. During her career, she earned $31,920 in earnings. Horses that haven't raced may show up with "Unraced" under their name.
Certain sires in a pedigree may show up with letters in brackets after their year of birth. Fappiano is an example below "[IC]". These letters signify the Fappiano is a chef-de-race horse and they are used to calculate the dosage numbers above the pedigree "DP = 14-12-12-0-0 (38) DI = 5.33 CD = 1.05". Chef-de-race horses on this site are designated by Steve Roman and more information about dosage and how to use it as a breeding tool can be found at http://www.chef-de-race.com/.
Genetic Strength Values are another system to evaluated a horse's pedigree and try to quantify the pedigree. Below Believe It's name, you'll see a number in braces "(54.30)", this is Believe It's Grasp Rating. Above the pedigree, you'll see the GSV number "GSV = 71.10". GSV ratings and Grasp numbers were developed by George William Smith and you can find out more information about using these numbers at his Understanding the GSV page.
Ellen Parker is a pedigree researcher who has spent lots of time studying famous mares. She's comes out with a list of the 500 or so most influential mares of the last century. These Reine De Course (Queens of The Turf) mares are highlighted in the pedigree with a green star. For instance Gay Hostess is a Reine De Course mare. If you are serious about pedigrees, check out her site for some good articles and also some great books about famous broodmares.