The tigers have stripes because it is advantageous for them because they are an ambush predator and need good camouflage. The stripes are excellent camouflage for places that are shady, so the tiger can easily get close to its prey and attack it.
There's a very big possibility that the distant ancestors of the tigers did not had stripes. The reasons for that are different environment, but also that the stripes are actually a very rare type of pattern among the felidae family members.
As the environment started changing, the tigers needed to adapt to it, so they also needed a different camouflage. As some tigers in the population started to develop stripes, they were better hunters, thus were stronger, and seen as suitable mates for the females, as it would provide an offspring with the advantage that the male tiger has. Through this selection in the breeding process of mates that have advantageous camouflage patterns, the stripes were becoming more and more present, to the point where they totally pushed aside and eliminated the previously dominant camouflage pattern.
