There are several restrictions while you are on a trial. The reasons for all of them boil down to three letters. RMT: Real Money Transfer, i.e. those people that come into tha game for free and make ISK which they sell for real world money. For an indepth explanation of why that hurts the economy you can read the devblog here (out of game).

The restrictions are:

1) No ISK transferring while on a trial: So all those ISK farmers can't just pass on their ISK. This is mainly to prevent the laundering of ISK, rather than direct transfer to real players(after it has been through several hands it becomes progressively harder to track).

2) Some ships cannot be trained while on trial: To prevent the use of ships which could potentially make lot of money early on to an experienced player. The ships affected are ones which otherwise would be quick to train for.

3) You cannot launch two or more clients on the same computer if one of them is a trial: To prevent a player creating hundreds of alts to mine for him or creating a PVP fleet of alts.

4) You cannot join many chat channels while on trial: To prevent spamming of the chat channels by ISK spammers. If they are bugging you in corp chat try joining a player corp. In local you will just have to block them when they appear.