I'm not a nuclear policy expert, but I did sleep at Holiday Inn Express last night and all that jazz (basically, I go to dinner parties where I'm the dumbest person in the room by a factor of 10 and just try to listen a lot).
#1 - Iran (unlike Pakistan or India) is a signatory to the NPT, which is the basis to use heavy sanctions against them for failing to meet their treaty obligations. Everything that happens with Iran starts here - the NPT. Iran, however, has not ratified the additional protocol to the NPT (which would give the IAEA much greater monitoring and inspection capabilities through the entire fuel cycle).
#2 - The NPT allows for signatory states to have peaceful nuclear programs for domestic purposes. As a signatory of the NPT, Iran can build and use reactors for energy and research purposes and are guaranteed that right.
#3 - The sticking point begins with the second point. To operate a reactor for commercial power (what is generally called a "light water reactor") you only need to use 5% enriched uranium as fuel, and very few countries actually enrich their own uranium - most simply purchase it from one of the weapon states. There are only 13 states in the world that have the ability to enrich (there are 8 states with active weapons producing programs, for comparison). There is much debate over whether the NPT guarantees the ability to enrich fuel or just to use it, and this has been the key sticking point with Iran. They have maintained they have the right to enrich fuel to just below the break line for "highly enriched uranium" (which is at 20%) with no interference. This is acerbated by the fact that the main research reactor in Iran was provided by the USA in the 1960's and originally required HEU to operate (which was standard for reactors of that era). When the US stopped providing fuel after the revolution, Iran eventually worked with Argentina to redesign the reactor to use LEU at 19.75% enrichment as fuel. The fuel for this reactor has been a tool for Iran pushing for their ability to enrich to 20%.
#4 - Why does fuel enrichment matter? Because the actual process of building a nuclear weapon is fairly doable by any competent industrial nation provided enough time and effort. Hell, North Korea can't keep their lights on at night, but they managed it. They way that the international community has approached non-proliferation is to try and stall the longest parts of the process, so that a state can't build a bomb overnight. Enriching uranium to a high enough % for weapons purposes, in a large enough quantity, is a complicated and time consuming process. If Iran wanted to flip the switch and build a bomb, 20% is much closer to weapons grade than 5% (it's not a linear curve in terms of the process required ... it ramps up rapidly). Iran's insistence on being able to enrich LEU as a basic right meant they were building a large stockpile of raw material they could run to weapons grade much more quickly than is necessary for a purely peaceful program.
#5 - Iran was building a heavy water reactor (Arak or IR-40). While acceptable under the NPT for peaceful purposes (Canada uses them, for example) - heavy water reactors are extremely difficult to monitor compared to LWR. This is for two reasons - the first is that it uses raw uranium for fuel, so the fuel cycle isn't tracked under the NPT. It would be under the additional protocol, which gives the IAEA access to monitor mining and milling ... but Iran hasn't ratified that. Secondly, to remove spent fuel (which is what contains the plutonium you would want for weapons) from a LWR you must shut the reactor down and it's a very identifiable process that is easy to monitor. A heavy water reactor can have fuel added and removed during operation, which means it's nearly impossible to truly monitor effectively. There's a reason that HWR are basically the realm of weapons states only.
#6 - This agreement is a big step because the two biggest proliferation risks are reduced (Arak is shut down for the period of the agreement, and the 20% enriched LEU is being downblended to 5%) ... the time for Iran to "breakout" and build a bomb has been extended. That's huge. Also, by agreeing to downblend to 5% and not enrich above that point Iran has conceded that don't have an absolute right to enrich to the HEU breakpoint of 20%, and any future agreement will almost certainly see them capping enrichment at that 5% point for nuclear power purposes. The research reactor fuel will be treated separately, probably with some sort of fuel provisioning arrangement involving Russia where by Iran is guaranteed fuel to keep that reactor working. Lastly, this agreement basically gives the IAEA Additional Protocol access for the next 6 months (mining, milling and on demand 2 hour notice inspections) - meaning that Iran likely in the near future will fully ratify the AP. All of those are big, big steps in backing Iran further back from being able to build a weapon in the immediate future.
#7 - Final key detail ... Israel is one of only four countries in the world to not have signed the NPT. They do not have a treaty obligation to recognize Iran's right to possess peaceful nuclear power. The United States does (as does every nation in the world other than Israel, India, Pakistan and the South Sudan).
I'm personal friends with a number of IAEA inspectors, National Nuclear Security Agency people and the like. If my Facebook feed and conversations with some of them are any indication, they almost universally think this is a very good first step. It's nothing final by any means, but there is a light at the end of this tunnel, something that nearly everyone doubted even existed a little while back.