Conjugations are forms of verbs that are changed to agree with the subject that is doing the action described by the verb. Usually most of the word stays the same, but the endings change. Most conjugation systems follow some sort of pattern within the language.
Example: French verb for 'to eat'- "manger" (stem: mang) ("manger" is the infinitive of the verb. The infinitive is the un-conjugated form of the verb, literally the "to do" something form such as to walk, to play, to eat. In English one does not say "I like eat" one must say "I like to eat". In both English and French ("J'aime manger") the infinitive form of the verb would be used in this case.
|I eat||je mange (mang + e)|
|You(informal) eat||tu manges (mang + es)|
|He/She eats||il/elle mange (mang + e)|
|You(formal) eat||vous mangez (mang + ez)|
|We eat||nous mangeons (mang + eons)|
|They eat||ils/elles mangent (mang + ent)|
The pattern here is that the "er" is removed from the verb and replaced with a different ending depending on the subject(who's doing the eating). This pattern is good for many French conjugations, but not all, and in other languages, conjugation patterns are going to be very different.