BOARD GAME MECHANIC
This has to be a draw between drafting and tile placement and fortunately there are a few games that fit both of these!
Drafting is a mechanic in which you have a hand of cards from which you must pick one and then hand the rest to the player on your left (or right in some cases), you then receive a new hand of cards from the player to your right (or left). From these cards, you build up a a new hand/deck from which you build, take actions of place tiles. What I love about drafting is the assessing of a cards value to you in one given moment and what I mean by this is that one card (or tile) may be much better out of context of the wider game, but in any given situation you will often find yourself picking a card that seems less useful but actually fits much better into your overall game plan. This also means that games of this type are rarely played the same way each time, granting them a level of replayability that is hard to rival at times.
(As an aside, I first came to love drafting through Magic: the Gathering, a game I haven't played for a while now, but one I can heartily recommend partaking in booster drafts with your friends if you prefer card games to board games.)
(Sushi Go! Party)
Tile Placement is just how it sounds. This mechanic is often paired with drafting or simply by taking a random tile from the top of a pile and as a result in quite a simple mechanic to grasp compared to drafting. Another common theme with tile placement is bidding for tiles with points or in-game currency. However the mechanic is utilised, what draws me to it is the variety of ways any combination of tiles can work together (I think we are sensing a theme with my favourite mechanics!) and how best to fit them in your game. One of the most popular games using this mechanic is Carcassonne and for me that game perfectly epitomises how tile placement works....pick a tile then place it down in the best place to score you the most points.
(A completed game of Kingdomino)
As a board game player, replayability is high on my list of what I look for in a game and so to me these mechanics allow the game to provide just what I need from it. They also provide more skill based decision making than relying on luck (such as with roll and move games). True, it is luck that initially determines what you are given, but it is in that moment of choosing what is going to be best for you out of a limited selection that really does it for me and you do get to see a lot of the cards/tiles that are going around the board which means that each decision can, and will, be affected as a whole rather than by themselves.