There are a number of different terms for a female horse, depending on its age.
For comparison, see also male horse.
In addition to the terms which define a female horse based on age (see above), there are also terms which define a female horse based on function:
These terms overlap to a certain extent. For example, a female horse which is 3.5 years old can be described as either a mare (an adult horse) or a filly (a young horse), since as a young adult it falls into both definitions. Likewise, an adult female horse which is being used for breeding can be described as a mare (a general category) or a broodmare (a more specific category).
Also, as noted above, the age definitions are interpreted differently depending on who is using them. For example, a filly may be defined as under 4 years of age, but some horse organisations define a filly as being under 3 years of age while others use 5 years.
When calculating age, racing organisations tend to use a specific date (e.g. 1st January) regardless of the actual birthday. For example, a horse born on 1st May 2009 would be considered a year old on 1st January 2010 (rather than on 1st May 2010). The reason for this is that some races are for specific ages (e.g. 3-year olds only), while other races which accept multiple ages will handicap horses differently depending on their age. To have to track each horses actual birthday to determine if it is eligible to race and to calculate its handicap would be complex, so by using a common birthday for all horses one only needs to use the birth year, which is much simplier.