Well, Collisions work from DPs and as on wikipedia "the similarity between a visualisation of the algorithm and the Greek letter lambda ( λ ). The shorter stroke of the letter lambda corresponds to the sequence { x i }, since it starts from the position b to the right of x. Accordingly, the longer stroke corresponds to the sequence { y i }, which "collides with" the first sequence (just like the strokes of a lambda intersect) and then follows it subsequently. "

You know you have a collision if two different kangaroos start to output the same value.  Say K1 output 1,3,5,8,9 and K2 output 2,4,5,8,9 we know that between K1 and K2 after 3 or 2 they collide. We then can then refer to the tame kangaroo and correlate the input value of the wild one or as JeanLucPons put it himself "The program uses 2 herds of kangaroos, a tame herd and a wild herd. When 2 kangoroos (a wild one and a tame one) collide, the key can be solved". the actual outputs are normal public keys and the inputs are private keys.