Measuring heat effect of reaction
In an ideal world you would not have to do that. You'd simply wait until the reaction completes and then make a single measurement of temperature.

Too bad our world isn't ideal. The moment your reaction vessel becomes slightly hotter than the environment, it starts losing heat. If you wait for too long, it will cool all the way down to room temperature, so there will be nothing to measure in the first place. If you make your measurement in the first seconds so as not to let any heat escape, that's too early; the reaction has barely started. If you wait just until completion (which is a few minutes into the process, judging by your graph), that's too late, because by then some amount of heat is already lost.

So what do we do? We account for the loss. We assume that the temperature drop is linear (which of course is just an approximation, but still, it is much better than nothing), make a dozen or so measurements, build that trendline, and extend it to the origin. That's where your temperature would stop if there were no drop.

So it goes.