Let $S \subsetneq P$ be a sample.
Suppose that data about some individuals in $P$ are more easily accessible than data about others.
Then $S$ is a convenience sample if and only if the primary criterion for the construction of $S$ is the higher accessibility of data of certain individuals in $P$ over others.
That is, the objects in $S$ are the ones conveniently at hand.
It needs to be pointed out that the nature of the convenience of the data being sampled may in fact correlate with the population parameter being measured.
An example of this would be an exercise to gather a statistical sample of leg lengths of kangaroos, where the convenience sample would consist of all the kangaroos that you can catch by running after them.
Hence it is advisable to regard a convenience sample as unlikely to be a truly representative sample of the population being studied.