I would say it depends on what you mean by "office purposes".
If it is just general ordinary tasks like using spreadsheets, e-mails, web based applications, then a Core i3 will be fine. If you do a lot of statistical analysis or financial modelling then a quad core i7 CPU is the way to go.
Without getting too in depth about the different technical aspects of the Core i3 / i5 / i7 you just need to know the following:
#1 - The higher the CPU "model", the higher the clockspeed which affects performance. So generally speaking, Core i7 have higher clockspeeds than the Core i5 which means it can complete heavily computational tasks faster than the Core i5. The Core i3 have lower clockspeed of the three "models".
#2 - Core i3 CPUs only have 2 cores. Core i5 / i7 come in both 2 core and 4 core varieties. Two cores are fine for everyday tasks. Four cores are better when you run heavily computation tasks since the more cores there are the more data the CPU can process.
That's basically it. The Core i3 will suffice for the vast majority of people doing office work. Generally speaking though, I would recommend a dual core i5 CPU if you can afford it.