Initial Condition(s) are a set of conditions, or a condition on the solution which will permit us to find out that solution which we are after.  Initial conditions are frequently abbreviated of the form:

y(t₀) = y₀ and or y^(k)(t₀) = y_k

Thus, we can say, initial conditions are values of the solution or/and its derivative(s) at exact points. As we will notice eventually, solutions to "nice sufficient" differential equations are unique and thus only one solution will meet the specified conditions.

For a specified differential equation the number of initial conditions are needed, will depend on the order of the differential equation as we will notice.