The way I understand things, isn't the purpose of the clause essentially so that Liverpool need to inform Suarez of any bids which come in for him whatsoever, pretty much alerting him to any potentially interested clubs. Further to that, if a bid reaches a certain pre-determined price, say £40 million, then the club who have bid automatically receive the right to speak to the player and/or his representatives - although Liverpool are under no obligation to accept the offer.
At this point, Suarez may then hold talks with the club and decide either that they can't offer what he wants, or that he is in favour of joining them. The next step may then be that Suarez hands in a transfer request in an attempt to force the move, or that the bidding club increase their offer on the back of positive talks with the player.
In this case, Arsenal can now talk to Suarez if they've met the price in order to be allowed to hold talks with him, and if those talks go well and they can agree upon the basis of a contract, then Arsenal will probably go back with some more money.