In what type of athletics event would speed and velocity be equal to each other? This came up in my lecture, but I did not really understand it...

Speed is the ratio of distance traveled to time taken and is a scalar quantity (that is, has only magnitude, but no direction). In comparison, velocity is the ratio of displacement to time taken and is a vector quantity (that is, has both magnitude and direction). For an object to have the same speed and velocity, it must be moving in a straight line. Only in that situation, speed and velocity would be equal to each other.

In athletics, common events such as football, soccer, tennis, cricket, running, etc., all involve scenarios where distance traveled and displacement are different. Short distance swimming (although it is not a athletics event), in which the swimmer has to just swim from one end of the pool to the other can be considered a case where both speed and velocity are same. Similarly, in long jump, the distance traveled and displacement of the athlete are same and hence velocity and speed are same.

Hope this helps.