Since this and other similar questions get asked on a fairly frequent basis I have written up a quick guide which hopefully hits the salient points and which at the same time provides a reasonable synopsis of the position. Do let me know if I've missed anything of value. Assuming you think it's of value I'll sticky it in due course.
License considerations:

If you are a player then all you need is the demo license of Fantasy Grounds provided that the DM has an Ultimate license. If the DM only has a standard license then you will need a standard license too.
If you are a DM then having the Ultimate license will allow all of your players to join your game with only the demo license. If you have only a standard license then all of your players are going to need a standard license too.
The ONLY difference between a Standard and an Ultimate license is that with the latter players can join your game with only a demo license. There is absolutely no difference in the content included with either license. No 5e manuals (PHB, DMG, MM etc) are included in ANY license – they are all separate purchases.
What comes with the license?

With a demo license you can access the 5e SRD and basic rules (as from April 2018). This will allow you to create some basic characters with all of the limits that come with the SRD and basic rules (see below).
With a Standard or Ultimate license you get the 5^th edition ruleset built in, the D&D basic rules and the 5e SRD. The ruleset is what allows you to handle a game of 5e D&D. It allows you to handle character creation, combat and a multitude of other things. However it is only a tool – it does not include content such as the PHB etc.
With the Basic Rules and the SRD you can create characters, encounters, treasures and everything else that you would need to play a game of 5e. However these modules are very much cut down versions of the Players Handbook, Dungeon Masters Guide and Monster Manual. You will not get the following with the SRD; for characters most of the archetypes, backgrounds, race options and almost all of the feats are missing. For NPCs many of them are missing, as well as all of the background information and all of the artwork. For the DMG; many magic items are missing; all of the dungeon creation and alternative rules are missing as well as all of the treasure tables and many other things.
What do I really need to play 5e?

First of all this depends on whether you are a player or a DM. As a player the only thing you need is a demo or Standard license as noted above. You need nothing else, but see the information on the PHB below. Whilst it isn't necessary for you to own this you might want to in order to create characters offline (provided you have at least a standard license).
As a DM this is a more difficult decision. The three core rulebooks – the PHB, DMG and MM have all been written and optimised for Fantasy Grounds. This means that many features in the FG versions are not available in the paper version. So for convenience alone the purchases are worth it. However here’s some further information on how each of the three volumes might, or might not, be for you.
PHB:
Primarily the PHB is concerned with character creation and the rules for actually playing the game. If you own the PHB then you can make it available to your players so that they can create their characters. Full drag and drop functionality means that players can drag a class, race, background and equipment into their character sheet and (almost) everything will be set up for them ready to play.
Note, however, that the character sheet is not a character builder so some manual intervention is required to get the best out of the character.
The drag and drop functionality links sections of the character sheet to the Player’s Handbook so the player (or the DM) can click on these links to open the relevant section. Of all three of the core rulebooks the consensus is that the PHB is pretty much essential for its ease of use and functionality.
MM:
If you are going to be creating your own campaigns (as opposed to purchasing adventures) as a DM then the Monster Manual will be a very desirable module to own. All of the NPCs are in there complete with background information and full colour artwork that can be shared with players. NPCs from the MM can be dropped into encounters and from there onto the Combat Tracker and onto maps. Each will have a token representing the NPC as well as all the statistics, attacks and defences of the NPC. When placed on the CT the NPCs attacks, spells and other abilities will show up on the CT and as DM you will be able to use those by simply double clicking on the attack, ability or effect.
If you plan to use only published adventures then the MM is perhaps less of a necessity since all of the NPCs in those adventures will come with it.
DMG:
The Dungeons Master’s Guide contains information on how to create worlds, dungeons, campaigns, NPCs, treasures and other rewards as well as detailed guidance on running a game and generally how to be a DM. It also contains many pages of magic items and a huge number of tables for rolling up random treasures, dungeons, personalities and a host of other things.
Whether you need any of this might also depend on whether you intend to make up your own adventures or run published ones. However even if you fall into the latter category the lure of those magic items is great – and with a single roll of a dice you can create a treasure parcel down to the smallest detail. If you roll a sword it will tell you what kind of sword; if you roll a scroll it will tell you what scroll you got; or what gem; or what armour or what potion.
Wherever possible the tables in the DMG have been optimised for use in FG like this. You roll once and if the table entry directs you to roll elsewhere then that roll is made too.
In summary then, the three core rulebooks are not essential but depending on how you run your game it could make life a lot easier, give your players a host of options, give you easy access to information and rules as well as cutting prep time by a considerable amount. It is worth mentioning also that if you have the time and inclination you could add all of the information into Fantasy Grounds yourself and create your own modules for personal use.