Big O
Big O is used to to represent the general asymptotic growth of an algorithm. These algorithms are measured as a factor of O(n). When representing a function in Big O, it is common to leave out any constant factors of n as well as any other constant atomic operations. A function that runs in $3n^2 + 5$ will be represented as $O(n^2)$ since we only care about the asymptotic growth of a function.
Big Ω (Omega)
Big Ω is used to represent the lower bound of a function’s asymptotic growth. This means that Big Ω will give use the complexity of a functions best case scenario. Algorithms will be measure as a factor of Ω(n) and factor in atomic operations and constant multiples of n.
Big Θ (Theta)
Big Θ represents the average case or random case of a function. It gives us an idea of how an algorithm will perform in any case.
The relationship between Θ, Ω, O
Given a function f(n), Ω represents the lower bound of the function, O represents the upper bound, and Θ can represent the average case or any case:
$$ Ω(f(n)) ≤ Θ(f(n)) ≤ O(f(n)) $$
$$ Ω(n) <= Θ(n) <= O(n) $$