Tactics in a board game usually refer to short-term optimizations to get a better local position in the game. Strategy refers to your long-term plans, for combining the results of many shorter term interactions into a winning game.
Some games have only tactical considerations, or an emphasis on them, while some games are more amenable to long-range planning.
In the game of Go, for instance, you may study tactical issues such as life and death (whether you can save or kill a particular enclosed group) and tesuji (clever tactics for killing and splitting your opponents stones, or saving or connecting your own), while also important are strategic issue like positional judgement (figuring out in the middle game who is ahead, and where they are ahead), direction of play, and balancing between territory and influence. Effective strategic play must of course be built on solid tactical play, but it can determine who winds up having the advantage in most tactical battles, and who winds up with the most territory even if they lose small battles here and there.
The concept can apply to other games as well. Tactics will usually influence how you play best for one or a few turns in a row, while strategy guides what you are doing for the whole game; how you will win. Strategy is about what you are trying to do, and tactics how you are trying to do it.
In Settlers of Catan, some strategic options may be going for roads and settlements, to try and get the longest road and a lot of settlements (with just enough cities to allow you to build more), or your strategy may be going with cities and development cards, with just enough settlements to allow you to build the cities you need; or you might have a ports based strategy, in which you try and obtain favorable ports and can thus buy any resources you need. The tactics used to support these strategies may be somewhat different, but they will involve tricks for getting the best trade, blocking your opponent quickly so you can get to the space you need, proper placement of the robber to slow down someone else competing with you.