This is from Joseph Blitzstein, Introduction to Probability, pg 197, Question 20:
Let $X\sim \text{Bin}(100, 0.9)$.
For each of the following parts, construct an example showing that it is possible, or explain clearly why it is impossible. In this problem, $Y$ is a random variable on the same probability space as $X$; note that $X$ and $Y$ are not necessarily independent.
(a) Is it possible to have $Y\sim \text{Pois}(0.01)$ with $P(X \ge Y ) = 1$?
I would like to know what does $P(X \ge Y)$ mean in this context. Does it mean that for all values that $X$ and $Y$ take $P(X \ge Y) = 1$?
$X$ and $Y$ are random variables, and $P(X \ge Y)$ is the probability that $X$ is greater than or equal to $Y$. In this case your random variables are discrete, so if that probability is $1$, it does mean that $x$ is always than or equal to $y$ for all possible values $(x,y)$ of the pair $(X,Y)$.
Further hint: what are the possible values of $X$? What are the possible values of $Y$?