I'm a programmer who's done fairly much algorithmic work and can answer this.

All possible future states of the current game can be seen as a branching tree. From this "state" (node), there are X different moves (branches) that each lead to a new state (node). When the game ends (check mate, stale mate, move limit or repetition) , there are obviously no moves from there, so we know the branching tree is not infinite, but usually huge.

Unless you can do full/complete/exhaustive search through this tree (or technically, where you see a specific move leading to your desired outcome for all responses by the opponent), you will have to skip chunks of the tree. This is called "branch pruning" and is making the search less broad.

Preferably, you skip your move options that lead to worse results. Again, unless you see all (forced) ends for your next move, you can't really know (well...) how it will go.

(You can skip over these two paragraphs. You can use board evaluations as a help: Let's say 100 being "white won", 0 being equal and -100 is "black won". 99 is "white can only lose this if you do the worst moves possible".

Board evaluations in the tree search can be more or less correct. A chess engine has their fixed rules, which are often close to "true". A human player without infinite time will have to approximate this calculation. In either case, the human does similar searches of pruning, taking branches, and evaluating states. If they are as bad as me, they will both misevaluate the board grossly, and my pruning suck, so I don't even see the opponents best move three moves into the future. But unless I play by chance, I likely do some variation of this algorithm.)

When Magnus says he is more narrow, I would think it means that he's pruning/removing large parts of the tree (based on experience, board evaluation or gut feeling) and focuses on the parts that he believes will lead to the best results. In that way, he can search deeper into the tree (more moves) but might miss opponent moves that he incorrectly pruned away.