Implicant :
A normal product term that implies Y.
Example: For the function Y = AB + ABC + BC, the implicants are AB, ABC, and BC because if any one of those terms are true, then Y is true.
Prime Implicant :
An implicant of Y such that if any variable is removed from the implicant, the resulting term does not imply Y.
Example: Y = AB + ABC + BC
Prime Implicants: AB, BC
Not a prime implicant: ABC
ABC is not a prime implicant because the literal A can be removed to give BC and BC still implies Y. Conversely AB is not a prime implicant because you can't remove either A or B and have the remaining term still imply Y.
In truth tables the prime implicants are represented by the largest rectangular groups of ones that can be circled. If a smaller subgroup is circled, the smaller group is an implicant, but not a prime implicant.
Minterm:
Minterms are called products because they are the logical AND of a set of variables, and maxterms are called sums because they are the logical OR of a set of variables. These concepts are dual because of their complementary-symmetry relationship as expressed by De Morgan's laws.