What are the free trial restrictions?

The free trial is mostly restricted in social aspects and others such as:

• You can not send tells/whispers
• You can not add friends. (You can be added by someone who has the full game)
• You can not join a Free Company (Player Guilds)
• You can not invite other players to a party (You can be invited to a party by someone who has the full game)
• You can not use the Market Board
• You can not do PvP content (for now)
• Gil cap is 300k.

And various others

What you can do however:

• Play all the content that is included in the base game ARR (A Realm Reborn) and the critically acclaimed expansion heavensward.
• Level all base game and Heavensward expansion jobs to level 60.
• Enjoy some great music and amazing story!
• No time limit on the free trial

For a quicker rundown you can watch Zeplas' video here:

You can find the official restrictions list here: Square Enix Support Center